Least Common Multiple (LCM) of 108 and 153
The least common multiple (LCM) of 108 and 153 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 153?
First, calculate the GCD of 108 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 153 = 0 remainder 108 |
| 2 | 153 ÷ 108 = 1 remainder 45 |
| 3 | 108 ÷ 45 = 2 remainder 18 |
| 4 | 45 ÷ 18 = 2 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 36 | 180 |
| 173 and 62 | 10726 |
| 45 and 103 | 4635 |
| 119 and 11 | 1309 |
| 80 and 99 | 7920 |