Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
Free LCM Calculator determines the least common multiple (LCM) between 60 and 12 the smallest integer that is 60 that is divisible by both numbers.
Least Common Multiple (LCM) of 60 and 12 is 60.
LCM(60,12) = 60
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 60 and 12. First we will calculate the prime factors of 60 and 12.
Prime Factorization of 60
2 | 60 |
2 | 30 |
3 | 15 |
5 | 5 |
1 |
Prime factors of 60 are 2, 3,5. Prime factorization of 60 in exponential form is:
60 = 22×31×51
Prime Factorization of 12
2 | 12 |
2 | 6 |
3 | 3 |
1 |
Prime factors of 12 are 2,3. Prime factorization of 12 in exponential form is:
12 = 22×31
Now multiplying the highest exponent prime factors to calculate the LCM of 60 and 12.
LCM(60,12) = 22×31×51
LCM(60,12) = 60
Factors of 60
List of positive integer factors of 60 that divides 60 without a remainder.
1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 12
List of positive integer factors of 12 that divides 12 without a remainder.
1, 2, 3, 4, 6, 12
The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 60 and 12, than apply into the LCM equation.
GCF(60,12) = 12
LCM(60,12) = ( 60 × 12) / 12
LCM(60,12) = 720 / 12
LCM(60,12) = 60
(i) The LCM of 12 and 60 is associative
LCM of 60 and 12 = LCM of 12 and 60
1. What is the LCM of 60 and 12?
Answer: LCM of 60 and 12 is 60.
2. What are the Factors of 60?
Answer: Factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. There are 12 integers that are factors of 60. The greatest factor of 60 is 60.
3. What are the Factors of 12?
Answer: Factors of 12 are 1, 2, 3, 4, 6, 12. There are 6 integers that are factors of 12. The greatest factor of 12 is 12.
4. How to Find the LCM of 60 and 12?
Answer:
Least Common Multiple of 60 and 12 = 60
Step 1: Find the prime factorization of 60
60 = 2 x 2 x 3 x 5
Step 2: Find the prime factorization of 12
12 = 2 x 2 x 3
Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:
LCM = 60 = 2 x 2 x 3 x 5
Step 4: Therefore, the least common multiple of 60 and 12 is 60.