What is the Least Common Multiple of 69945 and 69960?

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 69945 and 69960 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69945 and 69960, than apply into the LCM equation.

GCF(69945,69960) = 15
LCM(69945,69960) = ( 69945 × 69960) / 15
LCM(69945,69960) = 4893352200 / 15
LCM(69945,69960) = 326223480

Least Common Multiple (LCM) of 69945 and 69960 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69945 and 69960. First we will calculate the prime factors of 69945 and 69960.

Prime Factorization of 69945

Prime Factorization of 69960

Now multiplying the highest exponent prime factors to calculate the LCM of 69945 and 69960.

LCM(69945,69960) = 3¹ × 5¹ × 4663¹ × 2³ × 11¹ × 53¹
LCM(69945,69960) = 326223480