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1 - <p>312 Learners</p>

1 + <p>338 Learners</p>

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

3 <p>The smallest positive integer that divides the numbers with no numbers left behind is the LCM of 56 and 70. Did you know? We apply LCM unknowingly in everyday situations like setting alarms and to synchronize traffic lights and when making music. In this article, let’s now learn to find LCMs of 56 and 70.</p>

4 <h2>What is LCM of 56 and 70</h2>

5 <p>We can find the LCM using listing<a>multiples</a>method,<a>prime factorization</a>method and the<a>long division</a>method. These methods are explained here, apply a method that fits your understanding well. </p>

6 <h3>LCM of 56 and 70 using listing multiples method</h3>

7 <p><strong>Step 1:</strong>List the multiples<a>of</a>each of the<a>numbers</a>; </p>

8 <p>56 = 56,112,168,224,280,…</p>

9 <p>70 = 70,140,210,280,…</p>

10 <p><strong>Step 2: </strong>Find the smallest number in both the lists </p>

11 <p>LCM (56,70) = 280</p>

12 <h3>LCM of 56 and 70 using prime factorization method</h3>

13 <p><strong>Step 1: </strong>Prime factorize the numbers </p>

14 <p>56 = 2×2×2×7 </p>

15 <p>70 = 7×5×2 </p>

16 <p><strong>Step 2: </strong>find highest<a>powers</a></p>

17 <p><strong>Step 3: </strong>Multiply the highest powers of the numbers</p>

18 <p>LCM(56,70) = 280</p>

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21 <h3>LCM of 56 and 70 using division method</h3>

20 <h3>LCM of 56 and 70 using division method</h3>

22 <ul><li>Write the numbers in a row </li>

21 <ul><li>Write the numbers in a row </li>

23 </ul><ul><li>Divide them with a common prime<a>factor</a></li>

22 </ul><ul><li>Divide them with a common prime<a>factor</a></li>

24 </ul><ul><li>Carry forward numbers that are left undivided </li>

23 </ul><ul><li>Carry forward numbers that are left undivided </li>

25 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

24 </ul><ul><li>Continue dividing until the<a>remainder</a>is ‘1’ </li>

26 </ul><ul><li>Multiply the divisors to find the LCM</li>

25 </ul><ul><li>Multiply the divisors to find the LCM</li>

27 </ul><ul><li>LCM (56,70) = 280 </li>

26 </ul><ul><li>LCM (56,70) = 280 </li>

28 </ul><h2>Common mistakes and how to avoid them in LCM of 56 and 70</h2>

27 </ul><h2>Common mistakes and how to avoid them in LCM of 56 and 70</h2>

29 <p>Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid! </p>

28 <p>Listed here are a few mistakes children may make when trying to find the LCM due to confusion or due to unclear understanding. Be mindful, understand, learn and avoid! </p>

30 <h3>Problem 1</h3>

29 <h3>Problem 1</h3>

31 <p>Find the missing number. If the LCM of 56 and a certain number is 280, what is the missing number?</p>

30 <p>Find the missing number. If the LCM of 56 and a certain number is 280, what is the missing number?</p>

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

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

33 <p>We know the formula:</p>

32 <p>We know the formula:</p>

34 <p>LCM(a, b)=a×b/GCD</p>

33 <p>LCM(a, b)=a×b/GCD</p>

35 <p>Where a=56, the LCM is 280, and we need to find b. The GCD of 56 and 70 is 14 (calculated by the Euclidean algorithm).</p>

34 <p>Where a=56, the LCM is 280, and we need to find b. The GCD of 56 and 70 is 14 (calculated by the Euclidean algorithm).</p>

36 <p>Let's solve for b:</p>

35 <p>Let's solve for b:</p>

37 <p>LCM(56,b)=280</p>

36 <p>LCM(56,b)=280</p>

38 <p> 56×b/GCD(56,b)=280</p>

37 <p> 56×b/GCD(56,b)=280</p>

39 <p>Assume GCD(56, b) = 1 (we'll check later). Now we solve:</p>

38 <p>Assume GCD(56, b) = 1 (we'll check later). Now we solve:</p>

40 <p>56×b=280</p>

39 <p>56×b=280</p>

41 <p> b= 280 /56=5</p>

40 <p> b= 280 /56=5</p>

42 <p>Thus, the missing number is 5. </p>

41 <p>Thus, the missing number is 5. </p>

43 <h3>Explanation</h3>

42 <h3>Explanation</h3>

44 <p>Find the GCD of 56 and 5, which is 1. This confirms that the missing number is correct. </p>

43 <p>Find the GCD of 56 and 5, which is 1. This confirms that the missing number is correct. </p>

45 <p>Well explained 👍</p>

44 <p>Well explained 👍</p>

46 <h3>Problem 2</h3>

45 <h3>Problem 2</h3>

47 <p>If the LCM of two numbers is 280, and the product of the two numbers is 3920, find the GCD of the two numbers.</p>

46 <p>If the LCM of two numbers is 280, and the product of the two numbers is 3920, find the GCD of the two numbers.</p>

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

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

49 <p>We know the relationship between LCM, GCD, and the product of two numbers:</p>

48 <p>We know the relationship between LCM, GCD, and the product of two numbers:</p>

50 <p>LCM(a, b)×GCD(a, b)=a×b</p>

49 <p>LCM(a, b)×GCD(a, b)=a×b</p>

51 <p>Given:</p>

50 <p>Given:</p>

52 <p>LCM(a, b)=280 and a×b=3920</p>

51 <p>LCM(a, b)=280 and a×b=3920</p>

53 <p>Substitute the known values into the formula:</p>

52 <p>Substitute the known values into the formula:</p>

54 <p>280×GCD(a, b)=3920</p>

53 <p>280×GCD(a, b)=3920</p>

55 <p>Solve for GCD(a, b):</p>

54 <p>Solve for GCD(a, b):</p>

56 <p>GCD(a,b)=3920/280=14 </p>

55 <p>GCD(a,b)=3920/280=14 </p>

57 <h3>Explanation</h3>

56 <h3>Explanation</h3>

58 <p> Thus, the GCD of the two numbers is 14. </p>

57 <p> Thus, the GCD of the two numbers is 14. </p>

59 <p>Well explained 👍</p>

58 <p>Well explained 👍</p>

60 <h3>Problem 3</h3>

59 <h3>Problem 3</h3>

61 <p>Find the smallest positive integer x such that the LCM of 56 and x is 840.</p>

60 <p>Find the smallest positive integer x such that the LCM of 56 and x is 840.</p>

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

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

63 <p>We use the formula for LCM:</p>

62 <p>We use the formula for LCM:</p>

64 <p>LCM(56,x)=56×x/GCD(56,x)=840</p>

63 <p>LCM(56,x)=56×x/GCD(56,x)=840</p>

65 <p><strong>Step 1:</strong>Prime factorize the numbers.</p>

64 <p><strong>Step 1:</strong>Prime factorize the numbers.</p>

66 <p>56=23×71</p>

65 <p>56=23×71</p>

67 <p>840=23×31×51×71 </p>

66 <p>840=23×31×51×71 </p>

68 <p><strong>Step 2:</strong>To have the LCM be 840, x must include at least the prime factors 3 and 5 (since they are in 840 but not in 56).</p>

67 <p><strong>Step 2:</strong>To have the LCM be 840, x must include at least the prime factors 3 and 5 (since they are in 840 but not in 56).</p>

69 <p>Therefore, x must include:</p>

68 <p>Therefore, x must include:</p>

70 <p>x=31×51 =15 </p>

69 <p>x=31×51 =15 </p>

71 <h3>Explanation</h3>

70 <h3>Explanation</h3>

72 <p>Thus, the smallest value of x is 15.</p>

71 <p>Thus, the smallest value of x is 15.</p>

73 <p>Well explained 👍</p>

72 <p>Well explained 👍</p>

74 <h2>FAQs on the LCM of 56 and 70</h2>

73 <h2>FAQs on the LCM of 56 and 70</h2>

75 <h3>1.Find the ratio of 56 and 70?</h3>

74 <h3>1.Find the ratio of 56 and 70?</h3>

76 <h3>2.How much is 56 of 70?</h3>

75 <h3>2.How much is 56 of 70?</h3>

77 <h3>3.What is the LCM of 54 and 70?</h3>

76 <h3>3.What is the LCM of 54 and 70?</h3>

78 <p>54 = 3×3×3×2</p>

77 <p>54 = 3×3×3×2</p>

79 <p>70 = 7×5×2</p>

78 <p>70 = 7×5×2</p>

80 <p>LCM(54,70) = 1890 </p>

79 <p>LCM(54,70) = 1890 </p>

81 <h3>4.List three common multiples of 70 and 56. ,What is the LCM of 55 and 70?</h3>

80 <h3>4.List three common multiples of 70 and 56. ,What is the LCM of 55 and 70?</h3>

82 <p>280,560 and 840. 280 is the LCM of the numbers. </p>

81 <p>280,560 and 840. 280 is the LCM of the numbers. </p>

83 <p>, 55 = 11×5 - 70 = 2×5×7 LCM(55,70) = 770</p>

82 <p>, 55 = 11×5 - 70 = 2×5×7 LCM(55,70) = 770</p>

84 <h2>Important glossaries for LCM of 56 and 70</h2>

83 <h2>Important glossaries for LCM of 56 and 70</h2>

85 <ul><li><strong>Multiple:</strong>the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. </li>

84 <ul><li><strong>Multiple:</strong>the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. </li>

86 </ul><ul><li><strong>Prime Factor:</strong>A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind. </li>

85 </ul><ul><li><strong>Prime Factor:</strong>A number with only two factors, 1 and the number. For example,7, its factors are only 1 and 7 and the number when divided by any other integer will leave a remainder behind. </li>

87 </ul><ul><li><strong>Prime Factorization:</strong>breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. </li>

86 </ul><ul><li><strong>Prime Factorization:</strong>breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. </li>

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

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

89 <p>▶</p>

88 <p>▶</p>

90 <h2>Hiralee Lalitkumar Makwana</h2>

89 <h2>Hiralee Lalitkumar Makwana</h2>

91 <h3>About the Author</h3>

90 <h3>About the Author</h3>

92 <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>

91 <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>

93 <h3>Fun Fact</h3>

92 <h3>Fun Fact</h3>

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

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