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 |
|---|---|
| 162 and 176 | 14256 |
| 160 and 82 | 6560 |
| 171 and 177 | 10089 |
| 47 and 105 | 4935 |
| 200 and 146 | 14600 |