What is the Least Common Multiple of 1040 and 1045?
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 (LCM) of 1040 and 1045 is 217360.
LCM(1040,1045) = 217360
Least Common Multiple of 1040 and 1045 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 1045, than apply into the LCM equation.
GCF(1040,1045) = 5
LCM(1040,1045) = ( 1040 × 1045) / 5
LCM(1040,1045) = 1086800 / 5
LCM(1040,1045) = 217360
Least Common Multiple (LCM) of 1040 and 1045 with Primes
Least common multiple can be found by multiplying the highest exponent prime factors of 1040 and 1045. First we will calculate the prime factors of 1040 and 1045.
Prime Factorization of 1040
Prime factors of 1040 are 2, 5, 13. Prime factorization of 1040 in exponential form is:
1040 = 24 × 51 × 131
Prime Factorization of 1045
Prime factors of 1045 are 5, 11, 19. Prime factorization of 1045 in exponential form is:
1045 = 51 × 111 × 191
Now multiplying the highest exponent prime factors to calculate the LCM of 1040 and 1045.
LCM(1040,1045) = 24 × 51 × 131 × 111 × 191
LCM(1040,1045) = 217360
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