LCM for 30 and 105

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What's the Least Common Multiple (LCM) of 30 and 105?

Answer

LCM of 30 and 105 is
210

First common multiples: 210, 420, 630, …

210 is divisible by both: 210 ÷ 30 = 7, 210 ÷ 105 = 2 — and 7 and 2 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/30 by 7 and of y/105 by 2.

30 = 2 × 3 × 5

105 = 3 × 5 × 7

Prime30105Highest power
22—2
3333
5555
7—77

— = power 0: the prime is not a factor of this number; the LCM takes it from the number that has it.

LCM = 2 × 3 × 5 × 7 = 210

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LCM Table

Number 1Number 2LCM
3042210
30431,290
304590
3046690
3050150
3055330
3056840
3057570
3058870
306060
3070210
3075150
3080240
3096480
30100300
30105210
30110330
30120120
30145870
30155930
30165330
30170510
30180180
301851,110
30195390
302151,290
302351,410
302383,570
30240240
302451,470

FAQ

What's the Least Common Multiple (LCM) of 30 and 105?

LCM of 30 and 105 is 210

How to find the LCM of 30 and 105 using prime factorization?

To find the LCM of 30 and 105, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 210.

What is the difference between LCM and GCF?

LCM (Least Common Multiple) is the smallest number divisible by both numbers, while GCF (Greatest Common Factor) is the largest number that divides both. For 30 and 105: LCM = 210, GCF = 15.

See Also