LCM for 8, 14 and 21

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

What's the Least Common Multiple (LCM) of 8, 14 and 21?

Answer

LCM of 8, 14 and 21 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 8, 14 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 14 and 21 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 8: 2 × 2 × 2 (exponent form: 23)

All Prime Factors of 14: 2 × 7 (exponent form: 2 × 7)

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

Prime factor81421Highest power
2232—23
3——33
7—777

LCM = 23 × 3 × 7 = 168

Checking the LCM of 8, 14 and 21 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(8, 14) = (8 × 14) ÷ 2 = 112 ÷ 2 = 56

LCM(56, 21) = (56 × 21) ÷ 7 = 1,176 ÷ 7 = 168

LCM(8, 14, 21) = 168

The pairs may be taken in any order — 14 and 21 first, then 8 — and the answer is the same 168. 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 8, 14 and 21? (The answer is: 168). Enter the first number (e.g. '8'), the second (e.g. '14') and the third (e.g. '21'), 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
6814168
781456
881456
8914504
81014280
81114616
81214168
81314728
8141456
81415840
81416112
81417952
81418504
814191,064
81420280
81421168
81422616
814231,288
81424168
814251,400
81426728
814271,512
8142856
814291,624
81430840
814311,736
81432224
814331,848
81434952
81435280

FAQ

What's the Least Common Multiple (LCM) of 8, 14 and 21?

LCM of 8, 14 and 21 is 168

How to find the LCM of 8, 14 and 21 by prime factorization?

Take every prime that appears in 8, 14 and 21 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 14 and 21 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 14 is 56, and the LCM of 56 and 21 is 168 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 168 divisible by 8, 14 and 21?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 14 and 168 ÷ 21 all come out whole. Any other common multiple of 8, 14 and 21 is a multiple of 168.

See Also