Least Common Multiple of 36 and 60

Least common multiple (LCM) of 36 and 60 is 180.

LCM(36,60) = 180

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

LCM Calculator and

Least Common Multiple of 36 and 60 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 36 and 60, than apply into the LCM equation.

GCF(36,60) = 12
LCM(36,60) = ( 36 × 60) / 12
LCM(36,60) = 2160 / 12
LCM(36,60) = 180

Least Common Multiple (LCM) of 36 and 60 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 36 and 60. First we will calculate the prime factors of 36 and 60.

Prime Factorization of 36

Prime factors of 36 are 2, 3. Prime factorization of 36 in exponential form is:

36 = 22 × 32

Prime Factorization of 60

Prime factors of 60 are 2, 3, 5. Prime factorization of 60 in exponential form is:

60 = 22 × 31 × 51

Now multiplying the highest exponent prime factors to calculate the LCM of 36 and 60.

LCM(36,60) = 22 × 32 × 51
LCM(36,60) = 180