LCM for 156, 195 and 390

"Least Common Multiple of 3 Numbers" Calculator
Least Common Multiple of
,
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What's the Least Common Multiple (LCM) of 156, 195 and 390?

Answer

LCM of 156, 195 and 390 is
780

(Seven hundred eighty)

780 is the smallest positive integer that 156, 195 and 390 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 156, 195 and 390 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 156: 2 × 2 × 3 × 13 (exponent form: 22 × 3 × 13)

All Prime Factors of 195: 3 × 5 × 13 (exponent form: 3 × 5 × 13)

All Prime Factors of 390: 2 × 3 × 5 × 13 (exponent form: 2 × 3 × 5 × 13)

Prime factor156195390Highest power
222—222
33333
5—555
1313131313

LCM = 22 × 3 × 5 × 13 = 780

Checking the LCM of 156, 195 and 390 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(156, 195) = (156 × 195) ÷ 39 = 30,420 ÷ 39 = 780

LCM(780, 390) = (780 × 390) ÷ 390 = 304,200 ÷ 390 = 780

LCM(156, 195, 390) = 780

The pairs may be taken in any order — 195 and 390 first, then 156 — and the answer is the same 780. 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 156, 195 and 390? (The answer is: 780). Enter the first number (e.g. '156'), the second (e.g. '195') and the third (e.g. '390'), 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
15619537519,500
15619537673,320
15619537722,620
15619537849,140
156195379295,620
15619538014,820
15619538199,060
156195382148,980
156195383298,740
15619538424,960
15619538560,060
156195386150,540
156195387100,620
15619538875,660
156195389303,420
156195390780
156195391304,980
15619539276,440
156195393102,180
156195394153,660
15619539561,620
15619539625,740
156195397309,660
156195398155,220
156195399103,740
15619540015,600
156195401312,780
15619540252,260
15619540324,180
15619540478,780

FAQ

What's the Least Common Multiple (LCM) of 156, 195 and 390?

LCM of 156, 195 and 390 is 780

How to find the LCM of 156, 195 and 390 by prime factorization?

Take every prime that appears in 156, 195 and 390 to the highest power it reaches in any one of them and multiply: 2² × 3 × 5 × 13 = 780.

Can you get the LCM of 156, 195 and 390 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 156 and 195 is 780, and the LCM of 780 and 390 is 780 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 780 divisible by 156, 195 and 390?

Yes, and by definition it is the smallest positive integer that is: 780 ÷ 156, 780 ÷ 195 and 780 ÷ 390 all come out whole. Any other common multiple of 156, 195 and 390 is a multiple of 780.

See Also