LCM for 9, 75 and 105

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What's the Least Common Multiple (LCM) of 9, 75 and 105?

Answer

LCM of 9, 75 and 105 is
1,575

First common multiples: 1,575; 3,150; 4,725; …

1,575 is divisible by all three: 1,575 ÷ 9 = 175; 1,575 ÷ 75 = 21; 1,575 ÷ 105 = 15 — and 175, 21 and 15 have no factor but 1 common to all of them, so no smaller number is. As a common denominator: multiply the top and bottom of x/9 by 175 and of y/75 by 21 and of z/105 by 15.

9 = 32

75 = 3 × 52

105 = 3 × 5 × 7

Prime975105Highest power
3323332
5—52552
7——77

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

LCM = 32 × 52 × 7 = 1,575

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LCM Table

1st2nd3rdLCM
97590450
9759120,475
9759220,700
975936,975
9759421,150
975954,275
975967,200
9759721,825
9759822,050
975992,475
975100900
97510122,725
9751027,650
97510323,175
97510423,400
9751051,575
97510623,850
97510724,075
9751082,700
97510924,525
9751104,950
9751118,325
97511225,200
97511325,425
9751148,550
9751155,175
97511626,100
9751172,925
97511826,550
97511926,775

FAQ

What's the Least Common Multiple (LCM) of 9, 75 and 105?

LCM of 9, 75 and 105 is 1,575

How to find the LCM of 9, 75 and 105 by prime factorization?

Take every prime that appears in 9, 75 and 105 to the highest power it reaches in any one of them and multiply: 3² × 5² × 7 = 1,575.

Can you get the LCM of 9, 75 and 105 two numbers at a time?

Yes. The LCM of 9 and 75 is 225, and the LCM of 225 and 105 is 1,575 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 1,575 divisible by 9, 75 and 105?

Yes, and by definition it is the smallest positive integer that is: 1,575 ÷ 9, 1,575 ÷ 75 and 1,575 ÷ 105 all come out whole. Any other common multiple of 9, 75 and 105 is a multiple of 1,575.

See Also