LCM for 8, 28 and 30

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

What's the Least Common Multiple (LCM) of 8, 28 and 30?

Answer

LCM of 8, 28 and 30 is
840

(Eight hundred forty)

840 is the smallest positive integer that 8, 28 and 30 all divide without a remainder — every other common multiple of the three is a multiple of it.

Finding the LCM of 8, 28 and 30 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 28: 2 × 2 × 7 (exponent form: 22 × 7)

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

Prime factor82830Highest power
22322223
3——33
5——55
7—7—7

LCM = 23 × 3 × 5 × 7 = 840

Checking the LCM of 8, 28 and 30 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, 28) = (8 × 28) ÷ 4 = 224 ÷ 4 = 56

LCM(56, 30) = (56 × 30) ÷ 2 = 1,680 ÷ 2 = 840

LCM(8, 28, 30) = 840

The pairs may be taken in any order — 28 and 30 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, 28 and 30? (The answer is: 840). Enter the first number (e.g. '8'), the second (e.g. '28') and the third (e.g. '30'), 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
81528840
81628112
81728952
81828504
819281,064
82028280
82128168
82228616
823281,288
82428168
825281,400
82628728
827281,512
8282856
828291,624
82830840
828311,736
82832224
828331,848
82834952
82835280
82836504
828372,072
828381,064
828392,184
82840280
828412,296
82842168
828432,408
82844616

FAQ

What's the Least Common Multiple (LCM) of 8, 28 and 30?

LCM of 8, 28 and 30 is 840

How to find the LCM of 8, 28 and 30 by prime factorization?

Take every prime that appears in 8, 28 and 30 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, 28 and 30 two numbers at a time?

Yes, and it is the check this page prints. The LCM of 8 and 28 is 56, and the LCM of 56 and 30 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, 28 and 30?

Yes, and by definition it is the smallest positive integer that is: 840 ÷ 8, 840 ÷ 28 and 840 ÷ 30 all come out whole. Any other common multiple of 8, 28 and 30 is a multiple of 840.

See Also