What is the Least Common Multiple of 9970 and 9984?

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 9970 and 9984 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 9970 and 9984, than apply into the LCM equation.

GCF(9970,9984) = 2
LCM(9970,9984) = ( 9970 × 9984) / 2
LCM(9970,9984) = 99540480 / 2
LCM(9970,9984) = 49770240

Least Common Multiple (LCM) of 9970 and 9984 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 9970 and 9984. First we will calculate the prime factors of 9970 and 9984.

Prime Factorization of 9970

Prime Factorization of 9984

Now multiplying the highest exponent prime factors to calculate the LCM of 9970 and 9984.

LCM(9970,9984) = 2⁸ × 5¹ × 997¹ × 3¹ × 13¹
LCM(9970,9984) = 49770240