LCM for 75 and 90

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What's the Least Common Multiple (LCM) of 75 and 90?

Answer

LCM of 75 and 90 is
450

First common multiples: 450; 900; 1,350; …

450 is divisible by both: 450 ÷ 75 = 6, 450 ÷ 90 = 5 — and 6 and 5 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/75 by 6 and of y/90 by 5.

75 = 3 × 52

90 = 2 × 32 × 5

Prime7590Highest power
2—22
333232
552552

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 32 × 52 = 450

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LCM Table

Number 1Number 2LCM
757575
75765,700
75775,775
75781,950
75795,925
75801,200
75812,025
75826,150
75836,225
75842,100
75851,275
75866,450
75872,175
75886,600
75896,675
7590450
75916,825
75926,900
75932,325
75947,050
75951,425
75962,400
75977,275
75987,350
75992,475
75100300
751017,575
751022,550
751037,725
751047,800

FAQ

What's the Least Common Multiple (LCM) of 75 and 90?

LCM of 75 and 90 is 450

How to find the LCM of 75 and 90 using prime factorization?

To find the LCM of 75 and 90, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 450.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 75 and 90: LCM = 450, GCF = 15.

See Also