What is the Least Common Multiple of 35700 and 35712?

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 35700 and 35712 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 35700 and 35712, than apply into the LCM equation.

GCF(35700,35712) = 12
LCM(35700,35712) = ( 35700 × 35712) / 12
LCM(35700,35712) = 1274918400 / 12
LCM(35700,35712) = 106243200

Least Common Multiple (LCM) of 35700 and 35712 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 35700 and 35712. First we will calculate the prime factors of 35700 and 35712.

Prime Factorization of 35700

Prime Factorization of 35712

Now multiplying the highest exponent prime factors to calculate the LCM of 35700 and 35712.

LCM(35700,35712) = 2⁷ × 3² × 5² × 7¹ × 17¹ × 31¹
LCM(35700,35712) = 106243200