LCM for 3, 6 and 21

"Least Common Multiple of 3 Numbers" Calculator

What's the Least Common Multiple (LCM) of 3, 6 and 21?

Answer

LCM of 3, 6 and 21 is

(Forty-two)

42 is the smallest positive integer that 3, 6 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 3, 6 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 3: 3 (exponent form: 3)

All Prime Factors of 6: 2 × 3 (exponent form: 2 × 3)

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

Prime factor	3	6	21	Highest power
2	—	2	—	2
3	3	3	3	3
7	—	—	7	7

LCM = 2 × 3 × 7 = 42

Checking the LCM of 3, 6 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(3, 6) = (3 × 6) ÷ 3 = 18 ÷ 3 = 6

LCM(6, 21) = (6 × 21) ÷ 3 = 126 ÷ 3 = 42

LCM(3, 6, 21) = 42

The pairs may be taken in any order — 6 and 21 first, then 3 — and the answer is the same 42. That is exactly why the two routes on this page agree.

Related Calculations

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 3, 6 and 21? (The answer is: 42). Enter the first number (e.g. '3'), the second (e.g. '6') 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

LCM Table

Number 1	Number 2	Number 3	LCM
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30
3	6	31	186
3	6	32	96
3	6	33	66
3	6	34	102
3	6	35	210

FAQ

What's the Least Common Multiple (LCM) of 3, 6 and 21?

LCM of 3, 6 and 21 is 42

How to find the LCM of 3, 6 and 21 by prime factorization?

Take every prime that appears in 3, 6 and 21 to the highest power it reaches in any one of them and multiply: 2 × 3 × 7 = 42.

Can you get the LCM of 3, 6 and 21 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 3 and 6 is 6, and the LCM of 6 and 21 is 42 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 42 divisible by 3, 6 and 21?

Yes, and by definition it is the smallest positive integer that is: 42 ÷ 3, 42 ÷ 6 and 42 ÷ 21 all come out whole. Any other common multiple of 3, 6 and 21 is a multiple of 42.

LCM for 3, 6 and 21

What's the Least Common Multiple (LCM) of 3, 6 and 21?

Finding the LCM of 3, 6 and 21 by Prime Factorization

Checking the LCM of 3, 6 and 21 Two Numbers at a Time

Related Calculations

See Also

About "Least Common Multiple of 3 Numbers" Calculator

LCM Table

FAQ

What's the Least Common Multiple (LCM) of 3, 6 and 21?

How to find the LCM of 3, 6 and 21 by prime factorization?

Can you get the LCM of 3, 6 and 21 two numbers at a time?

Is 42 divisible by 3, 6 and 21?

See Also

Number 1	Number 2	Number 3	LCM
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30
3	6	31	186
3	6	32	96
3	6	33	66
3	6	34	102
3	6	35	210

Number 1	Number 2	Number 3	LCM
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30
3	6	31	186
3	6	32	96
3	6	33	66
3	6	34	102
3	6	35	210

Number 1	Number 2	Number 3	LCM
3	6	6	6
3	6	7	42
3	6	8	24
3	6	9	18
3	6	10	30
3	6	11	66
3	6	12	12
3	6	13	78
3	6	14	42
3	6	15	30
3	6	16	48
3	6	17	102
3	6	18	18
3	6	19	114
3	6	20	60
3	6	21	42
3	6	22	66
3	6	23	138
3	6	24	24
3	6	25	150
3	6	26	78
3	6	27	54
3	6	28	84
3	6	29	174
3	6	30	30
3	6	31	186
3	6	32	96
3	6	33	66
3	6	34	102
3	6	35	210