lcm (526; 3,156) = ? Calculate LCM, the least common multiple of numbers. Result written as an integer and prime factorized

lcm (526; 3,156) = ?

Approach 1. Integer numbers divisibility:

Divide the larger number by the smaller one.


Notice that dividing our numbers leaves no remainder:


3,156 ÷ 526 = 6 + 0;


=> 3,156 = 526 × 6;


So, 3,156 is divisible by 526.


3,156 is a multiple of 526.


The smallest multiple of 3,156 is the number itself: 3,156.


Consequently, least common multiple:
lcm (526; 3,156) = 3,156;


lcm (526; 3,156) = 3,156 = 22 × 3 × 263;
3,156 is a multiple of 526

Approach 2. Integer numbers prime factorization:

Prime Factorization of a number: finding the prime numbers that multiply together to make that number.


526 = 2 × 263;
526 is not a prime, is a composite number;


3,156 = 22 × 3 × 263;
3,156 is not a prime, is a composite number;


* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.



Calculate the least common multiple, lcm:

Multiply all the prime factors, by the largest exponents (if any).


lcm (526; 3,156) = 22 × 3 × 263;



lcm (526; 3,156) = 22 × 3 × 263 = 3,156
3,156 has all the prime factors of the number 526

Final answer:
Least common multiple
lcm (526; 3,156) = 3,156 = 22 × 3 × 263
3,156 is divisible by 526. 3,156 is a multiple of 526.
3,156 has all the prime factors of the number 526

Why do we need the least common multiple?

In order to add, subtract or compare fractions you have to first build their denominators the same. This common denominator is nothing else than the least common multiple of fractions' denominators, also called the least common denominator, lcd.


By definition, the least common multiple of two integers, LCM, is the smallest positive integer larger than 0 that is a multiple of both.


More operations of this kind:


Online calculator: LCM, the least common multiple

The latest calculated values of the "least common multiple", LCM

lcm (526; 3,156) = ? Oct 28 02:00 UTC (GMT)
lcm (2,405; 21,726) = ? Oct 28 02:00 UTC (GMT)
lcm (720; 120) = ? Oct 28 02:00 UTC (GMT)
lcm (825; 819) = ? Oct 28 02:00 UTC (GMT)
lcm (62; 24) = ? Oct 28 02:00 UTC (GMT)
lcm (78; 3,446) = ? Oct 28 01:59 UTC (GMT)
lcm (35; 3,654) = ? Oct 28 01:59 UTC (GMT)
lcm (62; 24) = ? Oct 28 01:59 UTC (GMT)
lcm (415; 520) = ? Oct 28 01:59 UTC (GMT)
lcm (82; 115) = ? Oct 28 01:58 UTC (GMT)
lcm (4; 137) = ? Oct 28 01:58 UTC (GMT)
lcm (55; 11) = ? Oct 28 01:58 UTC (GMT)
lcm (55; 60) = ? Oct 28 01:58 UTC (GMT)
least common multiple, see more...

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

What is a prime number?

What is a composite number?

Prime numbers up to 1,000

Prime numbers up to 10,000

Sieve of Eratosthenes

Euclid's algorithm

Simplifying ordinary (common) math fractions (reducing to lower terms): steps to follow and examples