LCM for 14, 21 and 28

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 14, 21 and 28?

Answer

LCM of 14, 21 and 28 is
84

(Eighty-four)

84 is the smallest positive integer that 14, 21 and 28 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 14, 21 and 28 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 14: 2 × 7 (exponent form: 2 × 7)

All Prime Factors of 21: 3 × 7 (exponent form: 3 × 7)

All Prime Factors of 28: 2 × 2 × 7 (exponent form: 22 × 7)

Prime factor142128Highest power
22—2222
3—3—3
77777

LCM = 22 × 3 × 7 = 84

Checking the LCM of 14, 21 and 28 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(14, 21) = (14 × 21) ÷ 7 = 294 ÷ 7 = 42

LCM(42, 28) = (42 × 28) ÷ 14 = 1,176 ÷ 14 = 84

LCM(14, 21, 28) = 84

The pairs may be taken in any order — 21 and 28 first, then 14 — and the answer is the same 84. That is exactly why the two routes on this page agree.

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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 14, 21 and 28? (The answer is: 84). Enter the first number (e.g. '14'), the second (e.g. '21') and the third (e.g. '28'), 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
131421546
14142142
141521210
141621336
141721714
141821126
141921798
142021420
14212142
142122462
142123966
142124168
1421251,050
142126546
142127378
14212884
1421291,218
142130210
1421311,302
142132672
142133462
142134714
142135210
142136252
1421371,554
142138798
142139546
142140840
1421411,722
14214242

FAQ

What's the Least Common Multiple (LCM) of 14, 21 and 28?

LCM of 14, 21 and 28 is 84

How to find the LCM of 14, 21 and 28 by prime factorization?

Take every prime that appears in 14, 21 and 28 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 14, 21 and 28 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 14 and 21 is 42, and the LCM of 42 and 28 is 84 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 84 divisible by 14, 21 and 28?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 21 and 84 ÷ 28 all come out whole. Any other common multiple of 14, 21 and 28 is a multiple of 84.

See Also