188 LearnersLast updated on May 26th, 2025
LCM of 120 and 150
LCM is the smallest and a common multiple of the numbers 120 and 150. We often apply the LCM to solve problems that have in them fractions, percentages, time intervals and others. Below, we explain how we find the LCM of 120 and 150.
What is the LCM of 120 and 150?
LCM (120,150) = 600
There are many ways to find the LCM, let us look at the listing multiples method, prime factorization method and the division method.
LCM of 120 and 150 Using Listing the Multiples
Step 1: List multiples of the numbers;
120–120,240,360,480,600,…
150– 150,300,450,600,…
Step 2: Find the smallest common number
LCM(120,150) = 600
LCM of 120 and 150 Using Prime Factorization
Step 1: Prime factorize the numbers
120 = 2×2×2×3×5
150= 2×3×5×5
Step 2: Multiply highest powers
23×3×52 = 600
LCM(120,150) = 600
LCM of 120 and 150 Using Division Method
- Write the numbers in a row
- Divide them by their common prime factors
- Carry forward the numbers that are not divided by the previously chosen number
- Continue dividing until the remainder is ‘1’
- Multiply the divisors to find the LCM — 2×2×2×3×5×5 = 600
- LCM(120,150) = 600
Common mistakes to avoid while finding the LCM of 120 and 150
Listed here are a few mistakes that are frequently made when trying to find the LCM.
Mistake 1
Listing multiples incorrectly
one may incorrectly list 240 as a multiple of both 120 and 150 even if it is only a multiple of 120 due to an oversight.
LCM of 120 and 150 Examples
Problem 1
Two machines A and B complete a cycle in 120 and 150 minutes, respectively. After how many minutes will both machines complete their cycle together again?
The LCM(120, 150) = 600 minutes.
Explanation
Both machines will complete a cycle together in 600 minutes.
Problem 2
The LCM of two numbers is 36 and the sum is 21. Find the numbers.
LCM(a, b) = 36
a+b= 21
We know that, LCM(a, b)×HCF(a, b) =a×b
Let us assume that the numbers a and b are 8 and 10,
8+10 = 18, it is not equal to the sum given
Let us assume that the numbers a and b are 12 and 30,
30+12= 42, which is equal to the sum given
Product of 12 and 30;
30 ×12= 360
LCM(a, b)×HCF(a, b) =a×b
LCM (30,12)×HCF(30,12) =30×12
LCM of 30,12;
Prime factorization of 12 = 2×2×3
Prime factorization of 30 = 5×2×3
LCM(30,12) = 60
HCF of 30,12;
Factors of 30 = 1,2,3,5,6,10,15,30
Factors of 12 = 1,2,3,4,6,12
HCF(30,12) = 6
60×6 =30×12
360 =360
Explanation
We, by assuming that a and b are 12 and 30 respectively and verifying the same against the formula figures that the assumption is right and a=12,b=30.
Problem 3
If 120 items represent 20% of a total, and 150 items represent 25% of another total, what is the least common multiple of the totals?
20% = 120
Total = 120/ 0.2 = 600
25% = 150
Total = 150/0.25 = 600
Explanation
Thus, the LCM of the totals is 600.
FAQs on the LCM of 120 and 150
1.What is the HCF of 120 and 150?
2.What is the LCM of 125 and 150?
3.What is the LCM of 100,150 and 120.
4.What is the LCM of 45,120 and 150?
5.What is the LCM of 150 and 225?
6.How can children in India use numbers in everyday life to understand LCM of 120 and 150 ?
7.What are some fun ways kids in India can practice LCM of 120 and 150 with numbers?
8.What role do numbers and LCM of 120 and 150 play in helping children in India develop problem-solving skills?
9.How can families in India create number-rich environments to improve LCM of 120 and 150 skills?
Important glossaries for LCM of 120 and 150
- Multiple: product of a number and integer
- Prime Factor: a number whose factors are itself and 1
- Prime Factorization: breaking a large number into its prime factors
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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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