LCM for 50 and 105

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What's the Least Common Multiple (LCM) of 50 and 105?

Answer

LCM of 50 and 105 is
1,050

First common multiples: 1,050; 2,100; 3,150; …

1,050 is divisible by both: 1,050 ÷ 50 = 21; 1,050 ÷ 105 = 10 — and 21 and 10 share no factor but 1, so no smaller number is. As a common denominator: multiply the top and bottom of x/50 by 21 and of y/105 by 10.

50 = 2 × 52

105 = 3 × 5 × 7

Prime50105Highest power
22—2
3—33
552552
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 × 52 × 7 = 1,050

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LCM Table

Number 1Number 2LCM
50512,550
5055550
50561,400
5060300
5065650
5070350
50721,800
5075150
5080400
50882,200
5090450
50100100
501051,050
50120600
50125250
50130650
50140700
501451,450
50170850
50175350
50180900
501851,850
50200200
502052,050
502101,050
502401,200
502452,450
50250250
502601,300
502852,850

FAQ

What's the Least Common Multiple (LCM) of 50 and 105?

LCM of 50 and 105 is 1,050

How to find the LCM of 50 and 105 using prime factorization?

To find the LCM of 50 and 105, find all prime factors of both numbers, then multiply the highest power of each prime factor. The result is 1,050.

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 50 and 105: LCM = 1,050, GCF = 5.

See Also