What is the Least Common Multiple of 13760 and 13768?

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 13760 and 13768 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 13760 and 13768, than apply into the LCM equation.

GCF(13760,13768) = 8
LCM(13760,13768) = ( 13760 × 13768) / 8
LCM(13760,13768) = 189447680 / 8
LCM(13760,13768) = 23680960

Least Common Multiple (LCM) of 13760 and 13768 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 13760 and 13768. First we will calculate the prime factors of 13760 and 13768.

Prime Factorization of 13760

Prime Factorization of 13768

Now multiplying the highest exponent prime factors to calculate the LCM of 13760 and 13768.

LCM(13760,13768) = 2⁶ × 5¹ × 43¹ × 1721¹
LCM(13760,13768) = 23680960