Last updated on May 26th, 2025
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.
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.
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
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
Listed here are a few mistakes that are frequently made when trying to find the LCM.
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.
Both machines will complete a cycle together in 600 minutes.
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
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.
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
Thus, the LCM of the totals is 600.
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.
: She loves to read number jokes and games.