What is the Least Common Multiple of 364 and 374?

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 364 and 374 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 364 and 374, than apply into the LCM equation.

GCF(364,374) = 2
LCM(364,374) = ( 364 × 374) / 2
LCM(364,374) = 136136 / 2
LCM(364,374) = 68068

Least Common Multiple (LCM) of 364 and 374 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 364 and 374. First we will calculate the prime factors of 364 and 374.

Prime Factorization of 364

Prime Factorization of 374

Now multiplying the highest exponent prime factors to calculate the LCM of 364 and 374.

LCM(364,374) = 2² × 7¹ × 13¹ × 11¹ × 17¹
LCM(364,374) = 68068