What is the Least Common Multiple of 1250 and 1265?

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 1250 and 1265 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1250 and 1265, than apply into the LCM equation.

GCF(1250,1265) = 5
LCM(1250,1265) = ( 1250 × 1265) / 5
LCM(1250,1265) = 1581250 / 5
LCM(1250,1265) = 316250

Least Common Multiple (LCM) of 1250 and 1265 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1250 and 1265. First we will calculate the prime factors of 1250 and 1265.

Prime Factorization of 1250

Prime Factorization of 1265

Now multiplying the highest exponent prime factors to calculate the LCM of 1250 and 1265.

LCM(1250,1265) = 2¹ × 5⁴ × 11¹ × 23¹
LCM(1250,1265) = 316250