What is the Least Common Multiple of 190 and 208?

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 190 and 208 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 190 and 208, than apply into the LCM equation.

GCF(190,208) = 2
LCM(190,208) = ( 190 × 208) / 2
LCM(190,208) = 39520 / 2
LCM(190,208) = 19760

Least Common Multiple (LCM) of 190 and 208 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 190 and 208. First we will calculate the prime factors of 190 and 208.

Prime Factorization of 190

Prime Factorization of 208

Now multiplying the highest exponent prime factors to calculate the LCM of 190 and 208.

LCM(190,208) = 2⁴ × 5¹ × 19¹ × 13¹
LCM(190,208) = 19760