What is the Least Common Multiple of 70080 and 70096?

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 70080 and 70096 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 70080 and 70096, than apply into the LCM equation.

GCF(70080,70096) = 16
LCM(70080,70096) = ( 70080 × 70096) / 16
LCM(70080,70096) = 4912327680 / 16
LCM(70080,70096) = 307020480

Least Common Multiple (LCM) of 70080 and 70096 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 70080 and 70096. First we will calculate the prime factors of 70080 and 70096.

Prime Factorization of 70080

Prime Factorization of 70096

Now multiplying the highest exponent prime factors to calculate the LCM of 70080 and 70096.

LCM(70080,70096) = 2⁶ × 3¹ × 5¹ × 73¹ × 13¹ × 337¹
LCM(70080,70096) = 307020480