187 LearnersLast updated on May 26th, 2025
LCM of 56 and 70
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
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!
Mistake 1
Duplicating or skipping a factor
A factor may be missed when we prime factorize a number. Writing the prime factorization of 70 may be written as 3×5×5×5 instead of 7×5×2 accidentally.
LCM of 56 and 70 Examples
Problem 1
Find the missing number. If the LCM of 56 and a certain number is 280, what is the missing number?
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.
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.
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.
Problem 3
Find the smallest positive integer x such that the LCM of 56 and x is 840.
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.
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?
4.List three common multiples of 70 and 56. ,What is the LCM of 55 and 70?
5.How can children in United States use numbers in everyday life to understand LCM of 56 and 70 ?
6.What are some fun ways kids in United States can practice LCM of 56 and 70 with numbers?
7.What role do numbers and LCM of 56 and 70 play in helping children in United States develop problem-solving skills?
8.How can families in United States create number-rich environments to improve LCM of 56 and 70 skills?
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.
Explore More numbers
Previous to LCM of 56 and 70
About BrightChamps in United States
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.
