LCM of 56 and 70
2026-02-28 14:05 Diff
https://brightchamps.com/en-us/math/numbers/lcm-of-56-and-70

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Last updated on August 5, 2025

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.

What is LCM of 56 and 70

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

LCM of 56 and 70 using listing multiples method

Step 1: List the multiples of each of the numbers; 


56 = 56,112,168,224,280,…


70 = 70,140,210,280,…


Step 2: Find the smallest number in both the lists 


LCM (56,70) = 280

LCM of 56 and 70 using prime factorization method

Step 1: Prime factorize the numbers 


56 = 2×2×2×7 


70 = 7×5×2 


Step 2: find highest powers


Step 3: Multiply the highest powers of the numbers


LCM(56,70) = 280

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LCM of 56 and 70 using division method

  • Write the numbers in a row 
  • Divide them with a common prime factor
  • Carry forward numbers that are left undivided 
  • Continue dividing until the remainder is ‘1’ 
  • Multiply the divisors to find the LCM
  • LCM (56,70) = 280 
     

Common mistakes and how to avoid them in LCM of 56 and 70

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!
 

Problem 1

Find the missing number. If the LCM of 56 and a certain number is 280, what is the missing number?

Okay, lets begin

We know the formula:


LCM(a, b)=a×b/GCD

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).


Let's solve for b:


LCM(56,b)=280


 56×b/GCD(56,b)=280


Assume GCD(56, b) = 1 (we'll check later). Now we solve:


56×b=280


 b= 280​/56=5


Thus, the missing number is 5.
 

Explanation

Find the GCD of 56 and 5, which is 1. This confirms that the missing number is correct.
 

Well explained 👍

Problem 2

If the LCM of two numbers is 280, and the product of the two numbers is 3920, find the GCD of the two numbers.

Okay, lets begin

We know the relationship between LCM, GCD, and the product of two numbers:


LCM(a, b)×GCD(a, b)=a×b


Given:


LCM(a, b)=280 and a×b=3920


Substitute the known values into the formula:


280×GCD(a, b)=3920


Solve for GCD(a, b):


GCD(a,b)=3920/280=14
 

Explanation

 Thus, the GCD of the two numbers is 14.
 

Well explained 👍

Problem 3

Find the smallest positive integer x such that the LCM of 56 and x is 840.

Okay, lets begin

We use the formula for LCM:


LCM(56,x)=56×x/GCD(56,x)=840


Step 1: Prime factorize the numbers.


56=23×71


840=23×31×51×71 


Step 2: 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).


Therefore, x must include:


x=31×51 =15
 

Explanation

Thus, the smallest value of x is 15.

Well explained 👍

FAQs on the LCM of 56 and 70

1.Find the ratio of 56 and 70?

2.How much is 56 of 70?

3.What is the LCM of 54 and 70?

54 = 3×3×3×2


70 = 7×5×2


LCM(54,70) = 1890
 

4.List three common multiples of 70 and 56. ,What is the LCM of 55 and 70?

280,560 and 840. 280 is the LCM of the numbers. 
 

, 55 = 11×5 — 70 = 2×5×7 LCM(55,70) = 770

Important glossaries for LCM of 56 and 70

  • Multiple: the result after multiplication of a number and an integer. To explain, 75×5 =375; 375 is a multiple of 75. 
  • Prime Factor: 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. 
  • Prime Factorization: breaking a number down into its prime factors. For example, 60 is written as the product of 2×2×3×5. 
     

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Hiralee Lalitkumar Makwana

About the Author

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.

Fun Fact

: She loves to read number jokes and games.