What is the Least Common Multiple of 69990 and 70000?

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 69990 and 70000 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 69990 and 70000, than apply into the LCM equation.

GCF(69990,70000) = 10
LCM(69990,70000) = ( 69990 × 70000) / 10
LCM(69990,70000) = 4899300000 / 10
LCM(69990,70000) = 489930000

Least Common Multiple (LCM) of 69990 and 70000 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 69990 and 70000. First we will calculate the prime factors of 69990 and 70000.

Prime Factorization of 69990

Prime Factorization of 70000

Now multiplying the highest exponent prime factors to calculate the LCM of 69990 and 70000.

LCM(69990,70000) = 2⁴ × 3¹ × 5⁴ × 2333¹ × 7¹
LCM(69990,70000) = 489930000