LCM for 75 and 180

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What's the Least Common Multiple (LCM) of 75 and 180?

Answer

LCM of 75 and 180 is
900

First common multiples: 900; 1,800; 2,700; …

900 is divisible by both: 900 ÷ 75 = 12, 900 ÷ 180 = 5 — and 12 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 12 and of y/180 by 5.

75 = 3 × 52

180 = 22 × 32 × 5

Prime75180Highest power
2—2222
333232
552552

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

LCM = 22 × 32 × 52 = 900

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LCM Table

Number 1Number 2LCM
75165825
7516612,450
7516712,525
751684,200
7516912,675
751702,550
751714,275
7517212,900
7517312,975
751744,350
75175525
7517613,200
751774,425
7517813,350
7517913,425
75180900
7518113,575
7518213,650
751834,575
7518413,800
751852,775
751864,650
7518714,025
7518814,100
751894,725
751902,850
7519114,325
751924,800
7519314,475
7519414,550

FAQ

What's the Least Common Multiple (LCM) of 75 and 180?

LCM of 75 and 180 is 900

How to find the LCM of 75 and 180 using prime factorization?

To find the LCM of 75 and 180, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 900.

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 180: LCM = 900, GCF = 15.

See Also