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172 LearnersLast updated on November 29th, 2024
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
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?
Explanation
Problem 2
The LCM of y and 42 is 126. Find the value of y.
Explanation
Problem 3
If the GCD of 36 and 42 is 6, verify the relationship LCM (36,42) x GCD (36,42)=36 × 42.
Explanation
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.
Explanation
Problem 5
Find two numbers such that their LCM is 252 and one of them is 36.
Explanation
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?
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
: She loves to read number jokes and games.
