LCM for 75 and 120

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What's the Least Common Multiple (LCM) of 75 and 120?

Answer

LCM of 75 and 120 is
600

First common multiples: 600; 1,200; 1,800; …

600 is divisible by both: 600 ÷ 75 = 8, 600 ÷ 120 = 5 — and 8 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 8 and of y/120 by 5.

75 = 3 × 52

120 = 23 × 3 × 5

Prime75120Highest power
2—2323
3333
552552

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

LCM = 23 × 3 × 52 = 600

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LCM Table

Number 1Number 2LCM
75105525
751067,950
751078,025
751082,700
751098,175
751101,650
751112,775
751128,400
751138,475
751142,850
751151,725
751168,700
751172,925
751188,850
751198,925
75120600
751219,075
751229,150
751233,075
751249,300
75125375
751263,150
751279,525
751289,600
751293,225
751301,950
751319,825
751323,300
751339,975
7513410,050

FAQ

What's the Least Common Multiple (LCM) of 75 and 120?

LCM of 75 and 120 is 600

How to find the LCM of 75 and 120 using prime factorization?

To find the LCM of 75 and 120, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 600.

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 120: LCM = 600, GCF = 15.

See Also