LCM for 75 and 200

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What's the Least Common Multiple (LCM) of 75 and 200?

Answer

LCM of 75 and 200 is
600

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

600 is divisible by both: 600 ÷ 75 = 8, 600 ÷ 200 = 3 — and 8 and 3 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/200 by 3.

75 = 3 × 52

200 = 23 × 52

Prime75200Highest power
2—2323
33—3
5525252

— = 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
751852,775
751864,650
7518714,025
7518814,100
751894,725
751902,850
7519114,325
751924,800
7519314,475
7519414,550
75195975
7519614,700
7519714,775
751984,950
7519914,925
75200600
752015,025
7520215,150
7520315,225
752045,100
752053,075
7520615,450
752075,175
7520815,600
7520915,675
752101,050
7521115,825
7521215,900
752135,325
7521416,050

FAQ

What's the Least Common Multiple (LCM) of 75 and 200?

LCM of 75 and 200 is 600

How to find the LCM of 75 and 200 using prime factorization?

To find the LCM of 75 and 200, 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 200: LCM = 600, GCF = 25.

See Also