What is the Least Common Multiple of 32970 and 32984?

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.

Least Common Multiple of 32970 and 32984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 32970 and 32984, than apply into the LCM equation.

GCF(32970,32984) = 14
LCM(32970,32984) = ( 32970 × 32984) / 14
LCM(32970,32984) = 1087482480 / 14
LCM(32970,32984) = 77677320

Least Common Multiple (LCM) of 32970 and 32984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 32970 and 32984. First we will calculate the prime factors of 32970 and 32984.

Prime Factorization of 32970

Prime Factorization of 32984

Now multiplying the highest exponent prime factors to calculate the LCM of 32970 and 32984.

LCM(32970,32984) = 2³ × 3¹ × 5¹ × 7¹ × 157¹ × 19¹ × 31¹
LCM(32970,32984) = 77677320