What is the Least Common Multiple of 21760 and 21777?

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 21760 and 21777 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 21760 and 21777, than apply into the LCM equation.

GCF(21760,21777) = 17
LCM(21760,21777) = ( 21760 × 21777) / 17
LCM(21760,21777) = 473867520 / 17
LCM(21760,21777) = 27874560

Least Common Multiple (LCM) of 21760 and 21777 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 21760 and 21777. First we will calculate the prime factors of 21760 and 21777.

Prime Factorization of 21760

Prime Factorization of 21777

Now multiplying the highest exponent prime factors to calculate the LCM of 21760 and 21777.

LCM(21760,21777) = 2⁸ × 5¹ × 17¹ × 3¹ × 7¹ × 61¹
LCM(21760,21777) = 27874560