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Least Common Multiple

The least common multiple, aka lowest common multiple of aka lowest common multiple of two integers a and b is the smallest positive integer that is divisible by both a and b.

The term is usually denoted lcm(a,b).

The easiest way to calculate the least common multiple of two or more integers is using our tool below.

Least Common Multiple Calculator

The lcm is...

Please note that our app is not limited to two integers;

it employs the associative law lcm(a,lcm(b,c)) = law lcm(lcm(a,b),c).

Likewise important, the lowest common multiple is commutative:

lcm(a,b) = lcm(b,a)

For the sake of completion,

lcm(b,b) = b; Idempotence

lcm(a,gcd(a,b)) = a; Absorption

What does the Least Common Multiple Mean?

Definition: For two given whole numbers a and b, the LCM is the smallest positive whole number that is divisible by both a and b.

Example of Least Common Multiple

For example, the lcm of 4 and 6, lcm(4,6) = 12.

Usage: For mathematical operations such as addition, subtraction and comparison with simple fractions, we often employ the lcm of the denominators usually referred to as lowest common denominator.

For example: 1/4 + 1/6 = 3/12 + 2/12 = 5/12.

How do You Find the Least Common Multiple?

Formula: you may use the greatest common factor (gcf) to determine the lcm of two numbers:

lcm(a,b) = \frac{a \times b}{gcf(a,b)}

Alternatively, using prime factorization, the lcm is the product of multiplying the highest powers of each number expressed as prime number factorization.

Lcm(4,6) = 22 × 31 = 12.

Ahead is a chart with common values for your convenience.

Table

The aim of this table is to provide you with frequently searched lcms.

Integer 1Integer 2LCM
12824
6824
5840
81040
152060
8324
8972
82040
82424
151260
101260
101530
31030
15945
141070
1416112
201260
151890
241648
1019190
153030
22444
142142
2430120
61442

Next is the summary of our article.

Conclusion

Lcm(a,b) = the smallest positive integer that is divisible by both a and b.

This ends our article.

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Least Common Multiple

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