Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 120 and 180 the smallest integer that is 360 that is divisible by both numbers.
Least Common Multiple (LCM) of 120 and 180 is 360.
LCM(120,180) = 360
Least common multiple or lowest common denominator (LCD) can be calculated in three ways;
Least common multiple can be found by multiplying the highest exponent prime factors of 120 and 180. First we will calculate the prime factors of 120 and 180.
Prime Factorization of 120
2 | 120 |
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 120 are 2, 3,5. Prime factorization of 120 in exponential form is:
120 = 23×31×51
Prime Factorization of 180
2 | 180 |
2 | 90 |
3 | 45 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 180 are 2, 3,5. Prime factorization of 180 in exponential form is:
180 = 22×32×51
Now multiplying the highest exponent prime factors to calculate the LCM of 120 and 180.
LCM(120,180) = 23×32×51
LCM(120,180) = 360
Factors of 120
List of positive integer factors of 120 that divides 120 without a remainder.
1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120
Factors of 180
List of positive integer factors of 180 that divides 180 without a remainder.
1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 120 and 180, than apply into the LCM equation.
GCF(120,180) = 60
LCM(120,180) = ( 120 × 180) / 60
LCM(120,180) = 21600 / 60
LCM(120,180) = 360
(i) The LCM of 180 and 120 is associative
LCM of 120 and 180 = LCM of 180 and 120
1. What is the LCM of 120 and 180?
Answer: LCM of 120 and 180 is 360.
2. What are the Factors of 120?
Answer: Factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120. There are 16 integers that are factors of 120. The greatest factor of 120 is 120.
3. What are the Factors of 180?
Answer: Factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180. There are 18 integers that are factors of 180. The greatest factor of 180 is 180.
4. How to Find the LCM of 120 and 180?
Answer:
Least Common Multiple of 120 and 180 = 360
Step 1: Find the prime factorization of 120
120 = 2 x 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 180
180 = 2 x 2 x 3 x 3 x 5
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 360 = 2 x 2 x 2 x 3 x 3 x 5
Step 4: Therefore, the least common multiple of 120 and 180 is 360.