What is the Least Common Multiple of 87000 and 87008?

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 87000 and 87008 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 87000 and 87008, than apply into the LCM equation.

GCF(87000,87008) = 8
LCM(87000,87008) = ( 87000 × 87008) / 8
LCM(87000,87008) = 7569696000 / 8
LCM(87000,87008) = 946212000

Least Common Multiple (LCM) of 87000 and 87008 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 87000 and 87008. First we will calculate the prime factors of 87000 and 87008.

Prime Factorization of 87000

Prime Factorization of 87008

Now multiplying the highest exponent prime factors to calculate the LCM of 87000 and 87008.

LCM(87000,87008) = 2⁵ × 3¹ × 5³ × 29¹ × 2719¹
LCM(87000,87008) = 946212000