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2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>Least Common Multiple (LCM) is the smallest positive integer that is divisible by both 36 and 45. By learning the following tricks, you can learn the LCM of 36 and 45 easily.</p>

4 <h2>What Is the LCM of 36 and 45?</h2>

5 <p>The LCM of 36 and 45 is 180. How did we get to this answer, though? That’s what we’re going to learn. We also see how we can find the LCM of 2 or more<a>numbers</a>in different ways. </p>

6 <h2>How to find the LCM of 36 and 45?</h2>

7 <p>We have already read about how you can approach finding the LCM of 2 or more numbers. Here is a list of those methods which make it easy to find the LCMs:</p>

8 <p>Method 1: Listing of Multiples Method 2: Prime Factorization Method 3: Division Method</p>

9 <p>Now let us delve further into these three methods and how it benefits us. </p>

10 <h3>LCM of 36 and 45 Using Listing of Multiples Method</h3>

11 <p>In this method, we will list all the<a>multiples</a>of 36 and 45. Then we will try to find a multiple that is present in both numbers.</p>

12 <p>For example, </p>

13 <p>Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360,…</p>

14 <p>Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, 450,…</p>

15 <p>The LCM of 36 and 45 is 180. 180 is the smallest number which can be divisible by both 36 and 45. </p>

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18 <h3>LCM of 36 and 45 Using Prime Factorization</h3>

17 <h3>LCM of 36 and 45 Using Prime Factorization</h3>

19 <p>To find the LCM of 36 and 45 using the<a>prime factorization</a>method, we need to find out the prime<a>factors</a>of both the numbers. Then multiply the highest<a>powers</a>of the factors to get the LCM. </p>

18 <p>To find the LCM of 36 and 45 using the<a>prime factorization</a>method, we need to find out the prime<a>factors</a>of both the numbers. Then multiply the highest<a>powers</a>of the factors to get the LCM. </p>

20 <p>Prime Factors of 36 are: 22, 32</p>

19 <p>Prime Factors of 36 are: 22, 32</p>

21 <p>Prime Factors of 45 are: 32, 51</p>

20 <p>Prime Factors of 45 are: 32, 51</p>

22 <p>Multiply the highest power of both the factors: 22 × 32 × 51 = 2 × 2 × 3 × 3 × 5 = 180</p>

21 <p>Multiply the highest power of both the factors: 22 × 32 × 51 = 2 × 2 × 3 × 3 × 5 = 180</p>

23 <p>Therefore, the LCM of 36 and 45 is 180. </p>

22 <p>Therefore, the LCM of 36 and 45 is 180. </p>

24 <h3>LCM of 36 and 45 Using Division Method</h3>

23 <h3>LCM of 36 and 45 Using Division Method</h3>

25 <p>To calculate the LCM using the<a>division</a>method. We will divide the given numbers with their<a>prime numbers</a>. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the<a>remainder</a>becomes 1. By multiplying the prime factors, one can get LCM.</p>

24 <p>To calculate the LCM using the<a>division</a>method. We will divide the given numbers with their<a>prime numbers</a>. The prime numbers should at least divide any one of the given numbers. Divide the numbers till the<a>remainder</a>becomes 1. By multiplying the prime factors, one can get LCM.</p>

26 <p>For finding the LCM of 36 and 45 we will use the following method.</p>

25 <p>For finding the LCM of 36 and 45 we will use the following method.</p>

27 <p>By multiplying the prime divisors from the table, we will get the LCM of 36 and 45</p>

26 <p>By multiplying the prime divisors from the table, we will get the LCM of 36 and 45</p>

28 <p>2 × 2 × 3 × 3 × 5 = 180</p>

27 <p>2 × 2 × 3 × 3 × 5 = 180</p>

29 <p>The LCM of 36 and 45 is 180. </p>

28 <p>The LCM of 36 and 45 is 180. </p>

30 <h2>Common Mistakes and How to Avoid Them in LCM of 36 and 45.</h2>

29 <h2>Common Mistakes and How to Avoid Them in LCM of 36 and 45.</h2>

31 <p>Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes. </p>

30 <p>Mistakes are common when we are finding the LCM of numbers. By learning the following common mistakes, we can avoid the mistakes. </p>

32 <h3>Problem 1</h3>

31 <h3>Problem 1</h3>

33 <p>Find the missing number that would satisfy both conditions for the sequence of common multiples of 36 and 45 up to 540.Given sequence: 0, 180, 360, ?, 720.</p>

32 <p>Find the missing number that would satisfy both conditions for the sequence of common multiples of 36 and 45 up to 540.Given sequence: 0, 180, 360, ?, 720.</p>

34 <p>Okay, lets begin</p>

33 <p>Okay, lets begin</p>

35 <p>LCM (36, 45) = 180</p>

34 <p>LCM (36, 45) = 180</p>

36 <p>The sequence of multiples: 0, 180, 360</p>

35 <p>The sequence of multiples: 0, 180, 360</p>

37 <p>Missing number = 360+180=540 </p>

36 <p>Missing number = 360+180=540 </p>

38 <h3>Explanation</h3>

37 <h3>Explanation</h3>

39 <p>The missing figure can be found by adding LCM repeatedly. Here, 180 is added successively to complete the sequence up to the required range. </p>

38 <p>The missing figure can be found by adding LCM repeatedly. Here, 180 is added successively to complete the sequence up to the required range. </p>

40 <p>Well explained 👍</p>

39 <p>Well explained 👍</p>

41 <h3>Problem 2</h3>

40 <h3>Problem 2</h3>

42 <p>A person buys 36 pencils and 45 pens. If they wish to distribute both items in equal groups without remainder, what is the maximum number of groups they can make?</p>

41 <p>A person buys 36 pencils and 45 pens. If they wish to distribute both items in equal groups without remainder, what is the maximum number of groups they can make?</p>

43 <p>Okay, lets begin</p>

42 <p>Okay, lets begin</p>

44 <p>Find the GCF of 36 and 45:</p>

43 <p>Find the GCF of 36 and 45:</p>

45 <p>GCF=9</p>

44 <p>GCF=9</p>

46 <p>Divide the items into groups of 9 each:</p>

45 <p>Divide the items into groups of 9 each:</p>

47 <p>Pencils: 36÷9= 4 groups. Pens: 45÷9=5 groups. </p>

46 <p>Pencils: 36÷9= 4 groups. Pens: 45÷9=5 groups. </p>

48 <h3>Explanation</h3>

47 <h3>Explanation</h3>

49 <p>The GCF helps determine the largest number of groups possible for a shared divisor between items, showing how GCF and divisibility link in distribution. </p>

48 <p>The GCF helps determine the largest number of groups possible for a shared divisor between items, showing how GCF and divisibility link in distribution. </p>

50 <p>Well explained 👍</p>

49 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

50 <h3>Problem 3</h3>

52 <p>If a=36 and b=45, prove that the relationship LCM(a, b)×GCF(a, b)=a×b holds true.</p>

51 <p>If a=36 and b=45, prove that the relationship LCM(a, b)×GCF(a, b)=a×b holds true.</p>

53 <p>Okay, lets begin</p>

52 <p>Okay, lets begin</p>

54 <p>Find the GCF of 36 and 45:</p>

53 <p>Find the GCF of 36 and 45:</p>

55 <p>36 = 22 × 32 45 = 32 × 5</p>

54 <p>36 = 22 × 32 45 = 32 × 5</p>

56 <p>GCF = 32 = 9</p>

55 <p>GCF = 32 = 9</p>

57 <p>Find the LCM:</p>

56 <p>Find the LCM:</p>

58 <p>LCM = 180</p>

57 <p>LCM = 180</p>

59 <p>Verify the relationship:</p>

58 <p>Verify the relationship:</p>

60 <p>LCM (36, 45) × GCF (36, 45) = 180 × 9 = 1620 a × b = 36 × 45 = 1620</p>

59 <p>LCM (36, 45) × GCF (36, 45) = 180 × 9 = 1620 a × b = 36 × 45 = 1620</p>

61 <p>Therefore, LCM × GCF = Product of the numbers </p>

60 <p>Therefore, LCM × GCF = Product of the numbers </p>

62 <p>Thus, the relationship holds true. </p>

61 <p>Thus, the relationship holds true. </p>

63 <h3>Explanation</h3>

62 <h3>Explanation</h3>

64 <p>This example confirms that the product of LCM and GCF for any two numbers is equal to the product of the numbers themselves. Here, it’s verified with 36 and 45. </p>

63 <p>This example confirms that the product of LCM and GCF for any two numbers is equal to the product of the numbers themselves. Here, it’s verified with 36 and 45. </p>

65 <p>Well explained 👍</p>

64 <p>Well explained 👍</p>

66 <h2>FAQs on the LCM of 36 and 45</h2>

65 <h2>FAQs on the LCM of 36 and 45</h2>

67 <h3>1.What is the prime factorization of 36 and 45?</h3>

66 <h3>1.What is the prime factorization of 36 and 45?</h3>

68 <p>36 = 2 × 2 × 3 × 3 45 = 5 × 3 × 3 </p>

67 <p>36 = 2 × 2 × 3 × 3 45 = 5 × 3 × 3 </p>

69 <p>This is the prime factorization of the numbers 36 and 45. </p>

68 <p>This is the prime factorization of the numbers 36 and 45. </p>

70 <h3>2.What is the GCF of 36 and 45?</h3>

69 <h3>2.What is the GCF of 36 and 45?</h3>

71 <p>Factors of 36 - 1, 2, 3, 4, 6, 9, 18, 36 Factors of 45 - 1, 3, 5, 9, 15, 45 The GCF (36, 45) = 9. </p>

70 <p>Factors of 36 - 1, 2, 3, 4, 6, 9, 18, 36 Factors of 45 - 1, 3, 5, 9, 15, 45 The GCF (36, 45) = 9. </p>

72 <h3>3. What numbers go into 36 and 45?</h3>

71 <h3>3. What numbers go into 36 and 45?</h3>

73 <p>The numbers that go into another without remainders are factors. </p>

72 <p>The numbers that go into another without remainders are factors. </p>

74 <p>Factors of 36 - 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 45 - 1, 3, 5, 9, 15, 45. </p>

73 <p>Factors of 36 - 1, 2, 3, 4, 6, 9, 12, 18, 36. Factors of 45 - 1, 3, 5, 9, 15, 45. </p>

75 <h3>4.What is the number divisible by 36 and 45?</h3>

74 <h3>4.What is the number divisible by 36 and 45?</h3>

76 <p>180 is the first number that is divisible by both 36 and 45. </p>

75 <p>180 is the first number that is divisible by both 36 and 45. </p>

77 <h3>5.What is the prime factorization of the LCM of 36 and 45?</h3>

76 <h3>5.What is the prime factorization of the LCM of 36 and 45?</h3>

78 <p>LCM (36, 45) = 180. </p>

77 <p>LCM (36, 45) = 180. </p>

79 <p>We can break 180 into its prime factors 22 × 32 × 51 = 180. </p>

78 <p>We can break 180 into its prime factors 22 × 32 × 51 = 180. </p>

80 <h2>Important Glossaries for the LCM of 36 and 45</h2>

79 <h2>Important Glossaries for the LCM of 36 and 45</h2>

81 <ul><li><strong>Prime Number:</strong>Any number that has only 2 factors is called a prime number.For example, 5 and 7, only common factors are 1 and the number itself.</li>

80 <ul><li><strong>Prime Number:</strong>Any number that has only 2 factors is called a prime number.For example, 5 and 7, only common factors are 1 and the number itself.</li>

82 </ul><ul><li><strong>Composite Number:</strong>Any number that has more than 2 factors is called a composite number. For example, 4,8, and 10. </li>

81 </ul><ul><li><strong>Composite Number:</strong>Any number that has more than 2 factors is called a composite number. For example, 4,8, and 10. </li>

83 </ul><ul><li><strong>Prime Factorization:</strong>It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number. </li>

82 </ul><ul><li><strong>Prime Factorization:</strong>It is breaking down a number into smaller prime numbers, then multiplied together, giving the same number. </li>

84 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

83 </ul><p>What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math</p>

85 <p>▶</p>

84 <p>▶</p>

86 <h2>Hiralee Lalitkumar Makwana</h2>

85 <h2>Hiralee Lalitkumar Makwana</h2>

87 <h3>About the Author</h3>

86 <h3>About the Author</h3>

88 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

87 <p>Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.</p>

89 <h3>Fun Fact</h3>

88 <h3>Fun Fact</h3>

90 <p>: She loves to read number jokes and games.</p>

89 <p>: She loves to read number jokes and games.</p>