LCM for 8, 15 and 21

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

What's the Least Common Multiple (LCM) of 8, 15 and 21?

Answer

LCM of 8, 15 and 21 is
840

(Eight hundred forty)

840 is the smallest positive integer that 8, 15 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 15 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 15: 3 × 5 (exponent form: 3 × 5)

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

Prime factor81521Highest power
223——23
3—333
5—5—5
7——77

LCM = 23 × 3 × 5 × 7 = 840

Checking the LCM of 8, 15 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, 15) = (8 × 15) ÷ 1 = 120 ÷ 1 = 120

LCM(120, 21) = (120 × 21) ÷ 3 = 2,520 ÷ 3 = 840

LCM(8, 15, 21) = 840

The pairs may be taken in any order — 15 and 21 first, then 8 — and the answer is the same 840. 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 8, 15 and 21? (The answer is: 840). Enter the first number (e.g. '8'), the second (e.g. '15') 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
6815120
7815840
8815120
8915360
81015120
811151,320
81215120
813151,560
81415840
81515120
81516240
815172,040
81518360
815192,280
81520120
81521840
815221,320
815232,760
81524120
81525600
815261,560
815271,080
81528840
815293,480
81530120
815313,720
81532480
815331,320
815342,040
81535840

FAQ

What's the Least Common Multiple (LCM) of 8, 15 and 21?

LCM of 8, 15 and 21 is 840

How to find the LCM of 8, 15 and 21 by prime factorization?

Take every prime that appears in 8, 15 and 21 to the highest power it reaches in any one of them and multiply: 2³ × 3 × 5 × 7 = 840.

Can you get the LCM of 8, 15 and 21 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 15 is 120, and the LCM of 120 and 21 is 840 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 840 divisible by 8, 15 and 21?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 8, 840 ÷ 15 and 840 ÷ 21 all come out whole. Any other common multiple of 8, 15 and 21 is a multiple of 840.

See Also