LCM for 5, 7 and 21

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

What's the Least Common Multiple (LCM) of 5, 7 and 21?

Answer

LCM of 5, 7 and 21 is
105

(One hundred five)

105 is the smallest positive integer that 5, 7 and 21 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 5, 7 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 5: 5 (exponent form: 5)

All Prime Factors of 7: 7 (exponent form: 7)

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

Prime factor5721Highest power
3——33
55——5
7—777

LCM = 3 × 5 × 7 = 105

Checking the LCM of 5, 7 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(5, 7) = (5 × 7) ÷ 1 = 35 ÷ 1 = 35

LCM(35, 21) = (35 × 21) ÷ 7 = 735 ÷ 7 = 105

LCM(5, 7, 21) = 105

The pairs may be taken in any order — 7 and 21 first, then 5 — and the answer is the same 105. 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 5, 7 and 21? (The answer is: 105). Enter the first number (e.g. '5'), the second (e.g. '7') 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
567210
57735
578280
579315
571070
5711385
5712420
5713455
571470
5715105
5716560
5717595
5718630
5719665
5720140
5721105
5722770
5723805
5724840
5725175
5726910
5727945
5728140
57291,015
5730210
57311,085
57321,120
57331,155
57341,190
573535

FAQ

What's the Least Common Multiple (LCM) of 5, 7 and 21?

LCM of 5, 7 and 21 is 105

How to find the LCM of 5, 7 and 21 by prime factorization?

Take every prime that appears in 5, 7 and 21 to the highest power it reaches in any one of them and multiply: 3 × 5 × 7 = 105.

Can you get the LCM of 5, 7 and 21 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 5 and 7 is 35, and the LCM of 35 and 21 is 105 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

Is 105 divisible by 5, 7 and 21?

Yes, and by definition it is the smallest positive integer that is: 105 ÷ 5, 105 ÷ 7 and 105 ÷ 21 all come out whole. Any other common multiple of 5, 7 and 21 is a multiple of 105.

See Also