LCM for 14, 28 and 42

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

What's the Least Common Multiple (LCM) of 14, 28 and 42?

Answer

LCM of 14, 28 and 42 is
84

(Eighty-four)

84 is the smallest positive integer that 14, 28 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 14, 28 and 42 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

All Prime Factors of 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

Prime factor142842Highest power
2222222
3——33
77777

LCM = 22 × 3 × 7 = 84

Checking the LCM of 14, 28 and 42 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, 28) = (14 × 28) ÷ 14 = 392 ÷ 14 = 28

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

LCM(14, 28, 42) = 84

The pairs may be taken in any order — 28 and 42 first, then 14 — and the answer is the same 84. That is exactly why the two routes on this page agree.

Related Calculations

See Also

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, 28 and 42? (The answer is: 84). Enter the first number (e.g. '14'), the second (e.g. '28') and the third (e.g. '42'), 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
142728756
14282828
142829812
142830420
142831868
142832224
142833924
142834476
142835140
142836252
1428371,036
142838532
1428391,092
142840280
1428411,148
14284284
1428431,204
142844308
1428451,260
142846644
1428471,316
142848336
142849196
142850700
1428511,428
142852364
1428531,484
142854756
1428551,540
14285656

FAQ

What's the Least Common Multiple (LCM) of 14, 28 and 42?

LCM of 14, 28 and 42 is 84

How to find the LCM of 14, 28 and 42 by prime factorization?

Take every prime that appears in 14, 28 and 42 to the highest power it reaches in any one of them and multiply: 2² × 3 × 7 = 84.

Can you get the LCM of 14, 28 and 42 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 14 and 28 is 28, and the LCM of 28 and 42 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, 28 and 42?

Yes, and by definition it is the smallest positive integer that is: 84 ÷ 14, 84 ÷ 28 and 84 ÷ 42 all come out whole. Any other common multiple of 14, 28 and 42 is a multiple of 84.

See Also