209 LearnersLast updated on May 26th, 2025
LCM of 36 and 42
The meaning of least common factor (LCM) is to find the smallest number that divides any two integers evenly. LCM is used mainly in fractions to find a common number for both the integers. We use LCM for solving problems, lining up cycles or even synchronizing of events, also to schedule tasks in everyday life.
What is the LCM of 36 and 42?
We use LCM of 36 and 42 to find the smallest number that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 252 without leaving any remainder. LCM is used mainly in fractions to find a common number for both the integers.
How to find the LCM of 36 and 42?
The LCM of 36 and 42 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 36 and 42 using Division method:
In division method, we divide both the numbers, we begin with dividing side by side the smallest number. We continue dividing until we get a common number that divides both the numbers equally. It makes it easier for the children to focus on prime factors and identify them.
- 2 divides 36 and 42
- 3 divides 18 and 21
- 6 divides 6
- 7 divides 7
Now multiply the divisors : 2×3×6×7=252 which is the LCM.
LCM of 36 and 42 using Listing multiples:
Step 1:Start by listing multiples of both the numbers separately:
Multiples of 36 are 36,72,108,144,180,216,252,288,324,360…..
Multiples of 42 are 42,84,126,168,210,252,294,336,378…..
Step 2:The least common factor from the list is 252. Therefore, the LCM of 36 and 42 is 252.
LCM of 36 and 42 using Prime factorization:
Step 1:We part both the numbers unto factors:
Factor of 36: 22×32
Factors of 42: 3×2x7
Step 2:Take the powers of both the numbers and multiply together:
LCM=22x32x7=252.
Common Mistakes and How to Avoid Them in LCM of 36 and 42
While solving problems based on the LCM of 36 and 42, children fail to understand few concepts, to give an idea of the mistakes,given below are a few mistakes and solutions of how to avoid them:
Mistake 1
Stopping the division method way too soon.
Students sometimes stop dividing very soon, when they are not able to divide both the numbers with the same number. For example, we can divide14 by 2, but 15 isn't divisible by 2. To continue the dividing method until all the factors are found. The students should continue dividing until they find the common number that divides both the integers.
LCM of 36 and 42 Examples
Problem 1
Find the LCM of 36 and x if the LCM is 252. What is the value of x?
x=7.
Explanation
LCM(36,x)=252
Prime factors of 36: 22 × 32
252=22 x 32 × 7
Therefore, x must include 7.
x=7.
Problem 2
The LCM of y and 42 is 126. Find the value of y.
y = 18
Explanation
LCM(y,42)=126
Prime factors of 42: 2×3x7.
126=2. × 32.× 7
y=3 × 42/7 =18.
Problem 3
If the GCD of 36 and 42 is 6, verify the relationship LCM (36,42) x GCD (36,42)=36 × 42.
GCD(36,42)=6
LCM(36,42)=(36 × 42)/6 =252
Verify : 252 × 6= 36 × 42 =1512
Explanation
value of both is equal to 1512
Problem 4
If the LCM of two numbers a and b is given by LCM(a, b)=k, find k if a=36 and b=42.
k=252.
Explanation
LCM(36,42)=252
Thus, k=252.
Problem 5
Find two numbers such that their LCM is 252 and one of them is 36.
22 × 32 to 252
= 22 × 32 x7.
Explanation
The other number is 7.
FAQs on LCM of 36 and 42
1.What is the GCF of 36 and 42?
2.What is the LCM of 35 and 36?
3. Write the LCM of 36,42, and 72?
4.Write nine hundred and fifty thousand in numbers?
5.What is LCM of 36?
6.How can children in Bahrain use numbers in everyday life to understand LCM of 36 and 42?
7.What are some fun ways kids in Bahrain can practice LCM of 36 and 42 with numbers?
8.What role do numbers and LCM of 36 and 42 play in helping children in Bahrain develop problem-solving skills?
9.How can families in Bahrain create number-rich environments to improve LCM of 36 and 42 skills?
Important glossaries on the LCM of 36 and 42
- Prime Factor: A natural number or whole number which has factors that are 1 and itself. For Example, 3 is a prime number.
- Prime Factorization: The process of breaking down a number into its prime factors is called Prime Factorization. For example, the factorization of 14 is 2x7.
- Co-prime numbers: numbers which have the only positive divisor of them both as 1. For example, 6 and 7.
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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
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