LCM for 8, 42 and 84

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Least Common Multiple of
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What's the Least Common Multiple (LCM) of 8, 42 and 84?

Answer

LCM of 8, 42 and 84 is
168

(One hundred sixty-eight)

168 is the smallest positive integer that 8, 42 and 84 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 42 and 84 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 42: 2 × 3 × 7 (exponent form: 2 × 3 × 7)

All Prime Factors of 84: 2 × 2 × 3 × 7 (exponent form: 22 × 3 × 7)

Prime factor84284Highest power
22322223
3—333
7—777

LCM = 23 × 3 × 7 = 168

Checking the LCM of 8, 42 and 84 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, 42) = (8 × 42) ÷ 2 = 336 ÷ 2 = 168

LCM(168, 84) = (168 × 84) ÷ 84 = 14,112 ÷ 84 = 168

LCM(8, 42, 84) = 168

The pairs may be taken in any order — 42 and 84 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, 42 and 84? (The answer is: 168). Enter the first number (e.g. '8'), the second (e.g. '42') and the third (e.g. '84'), 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
842693,864
84270840
8427111,928
84272504
8427312,264
842746,216
842754,200
842763,192
842771,848
842782,184
8427913,272
842801,680
842814,536
842826,888
8428313,944
84284168
8428514,280
842867,224
842874,872
842881,848
8428914,952
842902,520
842912,184
842923,864
842935,208
842947,896
8429515,960
84296672
8429716,296
842981,176

FAQ

What's the Least Common Multiple (LCM) of 8, 42 and 84?

LCM of 8, 42 and 84 is 168

How to find the LCM of 8, 42 and 84 by prime factorization?

Take every prime that appears in 8, 42 and 84 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 7 = 168.

Can you get the LCM of 8, 42 and 84 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 42 is 168, and the LCM of 168 and 84 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, 42 and 84?

Yes, and by definition it is the smallest positive integer that is: 168 ÷ 8, 168 ÷ 42 and 168 ÷ 84 all come out whole. Any other common multiple of 8, 42 and 84 is a multiple of 168.

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