Calculate the least common multiple of numbers, LCM (65; 130)

Approach 1. Integer numbers divisibility. Approach 2. Integer numbers prime factorization.

Approach 1. Integer numbers divisibility:

Notice that dividing our numbers leaves no remainder:


130 ÷ 65 = 2 + 0;


So, 130 is divisible by 65.


So, 130 is a multiple of 65.


Consequently, least common multiple:


lcm (65; 130) = 130;

lcm (65; 130) = 130 = 2 × 5 × 13;
130 is divisible by 65

Integer numbers divisibility


Approach 2. Integer numbers prime factorization:

65 = 5 × 13;


130 = 2 × 5 × 13;


Take all the prime factors, by the largest exponents.


Least common multiple:


lcm (65; 130) = 2 × 5 × 13;

lcm (65; 130) = 2 × 5 × 13 = 130
130 has all the prime factors of the number 65

Integer numbers prime factorization


Final answer:

Least common multiple:
lcm (65; 130) = 130 = 2 × 5 × 13;
130 is divisible by 65. 130 is a multiple of 65.
130 has all the prime factors of the number 65

lcm (65; 2,607) = ?

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Tutoring: what is it and how to calculate the least common multiple LCM of integer numbers

60 is a common multiple of the numbers 6 and 15, because 60 is a multiple of 6 and is also a multiple of 15. But there is also an infinite number of common multiples of 6 and 15.

If "v" is a multiple of "a" and "b", then all the multiples of "v" are also multiples of "a" and "b".

Common multiples of 6 and 15 are: 30, 60, 90, 120... Among them, 30 is the lowest and we say that 30 is the least common multiple, or the lowest common multiple, or the smallest common multiple of 6 and 15, abbreviated as LCM.

If e = LCM (a; b), then "e" contains all the prime factors involved in the prime factorizations of both "a" and "b", by the highest powers (exponents).

Based on this rule we can calculate the least common multiple, LCM, of the three numbers in the example below:

  • 40 = 23 × 5
  • 36 = 22 × 32
  • 126 = 2 × 32 × 7
  • LCM (40; 36; 126) = 23 × 32 × 5 × 7 = 2,520