LCM for 72 and 75

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What's the Least Common Multiple (LCM) of 72 and 75?

Answer

LCM of 72 and 75 is
1,800

First common multiples: 1,800; 3,600; 5,400; …

1,800 is divisible by both: 1,800 ÷ 72 = 25; 1,800 ÷ 75 = 24 — and 25 and 24 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/72 by 25 and of y/75 by 24.

72 = 23 × 32

75 = 3 × 52

Prime7275Highest power
223—23
332332
5—5252

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

LCM = 23 × 32 × 52 = 1,800

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LCM Table

Number 1Number 2LCM
7260360
72614,392
72622,232
7263504
7264576
72654,680
7266792
72674,824
72681,224
72691,656
72702,520
72715,112
727272
72735,256
72742,664
72751,800
72761,368
72775,544
7278936
72795,688
7280720
7281648
72822,952
72835,976
7284504
72856,120
72863,096
72872,088
7288792
72896,408

FAQ

What's the Least Common Multiple (LCM) of 72 and 75?

LCM of 72 and 75 is 1,800

How to find the LCM of 72 and 75 using prime factorization?

To find the LCM of 72 and 75, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 1,800.

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 72 and 75: LCM = 1,800, GCF = 3.

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