What is the Least Common Multiple of 1040 and 1054?

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 1040 and 1054 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 1040 and 1054, than apply into the LCM equation.

GCF(1040,1054) = 2
LCM(1040,1054) = ( 1040 × 1054) / 2
LCM(1040,1054) = 1096160 / 2
LCM(1040,1054) = 548080

Least Common Multiple (LCM) of 1040 and 1054 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 1040 and 1054. First we will calculate the prime factors of 1040 and 1054.

Prime Factorization of 1040

Prime Factorization of 1054

Now multiplying the highest exponent prime factors to calculate the LCM of 1040 and 1054.

LCM(1040,1054) = 2⁴ × 5¹ × 13¹ × 17¹ × 31¹
LCM(1040,1054) = 548080