LCM for 50, 56 and 105

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 50, 56 and 105?

Answer

LCM of 50, 56 and 105 is

4,200

First common multiples: 4,200; 8,400; 12,600; …

4,200 is divisible by all three: 4,200 ÷ 50 = 84; 4,200 ÷ 56 = 75; 4,200 ÷ 105 = 40 — and 84, 75 and 40 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/50 by 84 and of y/56 by 75 and of z/105 by 40.

50 = 2 × 5²

56 = 2³ × 7

105 = 3 × 5 × 7

Prime	50	56	105	Highest power
2	2	2³	—	2³
3	—	—	3	3
5	5²	—	5	5²
7	—	7	7	7

— = 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 × 7 = 4,200

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LCM Table

1st	2nd	3rd	LCM
50	56	90	12,600
50	56	91	18,200
50	56	92	32,200
50	56	93	130,200
50	56	94	65,800
50	56	95	26,600
50	56	96	16,800
50	56	97	135,800
50	56	98	9,800
50	56	99	138,600
50	56	100	1,400
50	56	101	141,400
50	56	102	71,400
50	56	103	144,200
50	56	104	18,200
50	56	105	4,200
50	56	106	74,200
50	56	107	149,800
50	56	108	37,800
50	56	109	152,600
50	56	110	15,400
50	56	111	155,400
50	56	112	2,800
50	56	113	158,200
50	56	114	79,800
50	56	115	32,200
50	56	116	40,600
50	56	117	163,800
50	56	118	82,600
50	56	119	23,800

FAQ

What's the Least Common Multiple (LCM) of 50, 56 and 105?

LCM of 50, 56 and 105 is 4,200

How to find the LCM of 50, 56 and 105 by prime factorization?

Take every prime that appears in 50, 56 and 105 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5² × 7 = 4,200.

Can you get the LCM of 50, 56 and 105 two numbers at a time?

Yes. The LCM of 50 and 56 is 1,400, and the LCM of 1,400 and 105 is 4,200 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 4,200 divisible by 50, 56 and 105?

Yes, and by definition it is the smallest positive integer that is: 4,200 ÷ 50, 4,200 ÷ 56 and 4,200 ÷ 105 all come out whole. Any other common multiple of 50, 56 and 105 is a multiple of 4,200.

LCM for 50, 56 and 105

What's the Least Common Multiple (LCM) of 50, 56 and 105?

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See Also

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 50, 56 and 105?

How to find the LCM of 50, 56 and 105 by prime factorization?

Can you get the LCM of 50, 56 and 105 two numbers at a time?

Is 4,200 divisible by 50, 56 and 105?

See Also