LCM for 50, 56 and 105

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

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

Answer

LCM of 50, 56 and 105 is
4,200

(Four thousand two hundred)

4,200 is the smallest positive integer that 50, 56 and 105 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 50, 56 and 105 by Prime Factorization

Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

All Prime Factors of 50: 2 × 5 × 5 (exponent form: 2 × 52)

All Prime Factors of 56: 2 × 2 × 2 × 7 (exponent form: 23 × 7)

All Prime Factors of 105: 3 × 5 × 7 (exponent form: 3 × 5 × 7)

Prime factor5056105Highest power
2223—23
3——33
552—552
7—777

LCM = 23 × 3 × 52 × 7 = 4,200

Checking the LCM of 50, 56 and 105 Two Numbers at a Time

The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

LCM(a, b) = (a × b) ÷ GCD(a, b)

LCM(50, 56) = (50 × 56) ÷ 2 = 2,800 ÷ 2 = 1,400

LCM(1,400, 105) = (1,400 × 105) ÷ 35 = 147,000 ÷ 35 = 4,200

LCM(50, 56, 105) = 4,200

The pairs may be taken in any order — 56 and 105 first, then 50 — and the answer is the same 4,200. That is exactly why the two routes on this page agree.

Related Calculations

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About "Least Common Multiple of 3 Numbers" Calculator

This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 50, 56 and 105? (The answer is: 4,200). Enter the first number (e.g. '50'), the second (e.g. '56') and the third (e.g. '105'), then hit the 'Calculate' button.
The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
and

LCM Table

Number 1Number 2Number 3LCM
50569012,600
50569118,200
50569232,200
505693130,200
50569465,800
50569526,600
50569616,800
505697135,800
5056989,800
505699138,600
50561001,400
5056101141,400
505610271,400
5056103144,200
505610418,200
50561054,200
505610674,200
5056107149,800
505610837,800
5056109152,600
505611015,400
5056111155,400
50561122,800
5056113158,200
505611479,800
505611532,200
505611640,600
5056117163,800
505611882,600
505611923,800

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, and it is the check this page prints. 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.

See Also