Least Common Multiple (LCM) of 108 and 51
The least common multiple (LCM) of 108 and 51 is 1836.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 108 and 51?
First, calculate the GCD of 108 and 51 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 51 = 2 remainder 6 |
| 2 | 51 ÷ 6 = 8 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 113 | 15481 |
| 122 and 103 | 12566 |
| 162 and 126 | 1134 |
| 116 and 173 | 20068 |
| 153 and 70 | 10710 |