149 LearnersLast updated on May 26th, 2025
LCM of 40,36 and 126
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 40,36 and 126?
We use LCM of 40,36 and 126 to find the smallest number that divides both the numbers equally. The smallest positive number is the number that divides both numbers equally, is 1260 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 40,36 and 126?
The LCM of 40,36 and 126 can be found by the following methods like division method, listing multiples, prime factorization.
LCM of 40,36 and 126 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 40,36,126
- 2 divides 20,18,63
- 2 divides 10,9,63
- 3 divides 5,3,21
- 3 divides 5,1,7
- 5 divides 1,1,7
- 7 divides 1,1,1.
Now multiply the divisors : 2×2×2×3×3×5×7=1260 which is the LCM.
LCM of 40,36 and 126 using Listing multiples:
Start by listing multiples of both the numbers separately:
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, 400, 440, 480, 520, 560, 600...
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432...
Multiples of 126: 126, 252, 378, 504, 630, 756, 882, 1,008, 1,134, 1,260...
The least common factor from the list is 1260. Therefore, the LCM of 40,36, and 126 is 210.
LCM of 40,36 and 126 using Prime factorization:
We part both the numbers unto factors:
Factor of 40: 23×5
Factors of 36: 22×32
Take the powers of both the numbers and multiply together:
LCM=23x32x5x7=1260.
Common Mistakes and How to Avoid Them in LCM of 40,36 and 126
While solving problems based on the LCM of 40,36 and 126 , 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 40,36 and 126 Examples
Problem 1
Find the product of two numbers if their LCM is 252 and their GCD is 18.
Formula: LCM(a, b) x GCD(a, b)= a × b
252 × 18 =4536
Explanation
The product of the two numbers is 4536.
Problem 2
If a=40 and LCM(a, b)=360, find b.
Answer: b = 9.
Explanation
LCM(a, b)= ab/GCD(a,b)
LCM(40,b)=360
GCD(40,b)=1
360= 40 × b/1
b=9.
Problem 3
If the LCM of 36, 40, and a number z is 5040, find the smallest value of z.
z=7.
Explanation
LCM(36, 40) = 360
LCM(360, z) = 5040
z must contain the missing factor 7.
Thus, z=7.
Problem 4
What is the smallest 4-digit number divisible by the LCM of 40 and 126?
The smallest 4-digit number divisible by 2520 is 2520.
Explanation
LCM(40, 126) = 2520
Smallest 4-digit number is 1000.
Divide: 1000÷2520≈0.3961000 ÷ 2520 ≈ 0.3961000÷2520≈0.396,
so the first multiple is 2520 itself.
The smallest 4-digit number divisible by 2520 is 2520.
Problem 5
Find the sum of the first three multiples of the LCM of 36 and 126.
The sum is 1512.
Explanation
LCM(36, 126) = 252
First three multiples: 252, 504, 756
Sum = 252 + 504 + 756 = 1512
therefore, The sum is 1512.
FAQs on LCM of 40,36 and 126
1.What is the GCF of 84,90 and 120?
2.In mathematics, what is GCD?
3.Is zero a real number?
4.What are integers?
5. Are fractions integers ?
6.How can children in Qatar use numbers in everyday life to understand LCM of 40,36 and 126?
7.What are some fun ways kids in Qatar can practice LCM of 40,36 and 126 with numbers?
8.What role do numbers and LCM of 40,36 and 126 play in helping children in Qatar develop problem-solving skills?
9.How can families in Qatar create number-rich environments to improve LCM of 40,36 and 126 skills?
Important glossaries on the LCM of 40,36 and 126
- 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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About BrightChamps in Qatar
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.
