What is the Least Common Multiple of 31560 and 31565?

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 31560 and 31565 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 31560 and 31565, than apply into the LCM equation.

GCF(31560,31565) = 5
LCM(31560,31565) = ( 31560 × 31565) / 5
LCM(31560,31565) = 996191400 / 5
LCM(31560,31565) = 199238280

Least Common Multiple (LCM) of 31560 and 31565 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 31560 and 31565. First we will calculate the prime factors of 31560 and 31565.

Prime Factorization of 31560

Prime Factorization of 31565

Now multiplying the highest exponent prime factors to calculate the LCM of 31560 and 31565.

LCM(31560,31565) = 2³ × 3¹ × 5¹ × 263¹ × 59¹ × 107¹
LCM(31560,31565) = 199238280