What is the Least Common Multiple of 69804 and 69822?

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 69804 and 69822 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69804 and 69822, than apply into the LCM equation.

GCF(69804,69822) = 18
LCM(69804,69822) = ( 69804 × 69822) / 18
LCM(69804,69822) = 4873854888 / 18
LCM(69804,69822) = 270769716

Least Common Multiple (LCM) of 69804 and 69822 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69804 and 69822. First we will calculate the prime factors of 69804 and 69822.

Prime Factorization of 69804

Prime Factorization of 69822

Now multiplying the highest exponent prime factors to calculate the LCM of 69804 and 69822.

LCM(69804,69822) = 2² × 3⁴ × 7¹ × 277¹ × 431¹
LCM(69804,69822) = 270769716