LCM for 18, 30 and 42

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 18, 30 and 42?

Answer

LCM of 18, 30 and 42 is
630

(Six hundred thirty)

630 is the smallest positive integer that 18, 30 and 42 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 18, 30 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 18: 2 × 3 × 3 (exponent form: 2 × 32)

All Prime Factors of 30: 2 × 3 × 5 (exponent form: 2 × 3 × 5)

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

Prime factor183042Highest power
22222
3323332
5—5—5
7——77

LCM = 2 × 32 × 5 × 7 = 630

Checking the LCM of 18, 30 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(18, 30) = (18 × 30) ÷ 6 = 540 ÷ 6 = 90

LCM(90, 42) = (90 × 42) ÷ 6 = 3,780 ÷ 6 = 630

LCM(18, 30, 42) = 630

The pairs may be taken in any order — 30 and 42 first, then 18 — and the answer is the same 630. 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 18, 30 and 42? (The answer is: 630). Enter the first number (e.g. '18'), the second (e.g. '30') 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
182730270
1828301,260
1829302,610
18303090
1830312,790
1830321,440
183033990
1830341,530
183035630
183036180
1830373,330
1830381,710
1830391,170
183040360
1830413,690
183042630
1830433,870
1830441,980
18304590
1830462,070
1830474,230
183048720
1830494,410
183050450
1830511,530
1830522,340
1830534,770
183054270
183055990
1830562,520

FAQ

What's the Least Common Multiple (LCM) of 18, 30 and 42?

LCM of 18, 30 and 42 is 630

How to find the LCM of 18, 30 and 42 by prime factorization?

Take every prime that appears in 18, 30 and 42 to the highest power it reaches in any one of them and multiply: 2 × 3² × 5 × 7 = 630.

Can you get the LCM of 18, 30 and 42 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 18 and 30 is 90, and the LCM of 90 and 42 is 630 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 630 divisible by 18, 30 and 42?

Yes, and by definition it is the smallest positive integer that is: 630 ÷ 18, 630 ÷ 30 and 630 ÷ 42 all come out whole. Any other common multiple of 18, 30 and 42 is a multiple of 630.

See Also