What is the Least Common Multiple of 38 and 142?

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 38 and 142 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 38 and 142, than apply into the LCM equation.

GCF(38,142) = 2
LCM(38,142) = ( 38 × 142) / 2
LCM(38,142) = 5396 / 2
LCM(38,142) = 2698

Least Common Multiple (LCM) of 38 and 142 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 38 and 142. First we will calculate the prime factors of 38 and 142.

Prime Factorization of 38

Prime Factorization of 142

Now multiplying the highest exponent prime factors to calculate the LCM of 38 and 142.

LCM(38,142) = 2¹ × 19¹ × 71¹
LCM(38,142) = 2698