Least Common Multiple (LCM) of 140 and 108
The least common multiple (LCM) of 140 and 108 is 3780.
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 140 and 108?
First, calculate the GCD of 140 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 108 = 1 remainder 32 |
| 2 | 108 ÷ 32 = 3 remainder 12 |
| 3 | 32 ÷ 12 = 2 remainder 8 |
| 4 | 12 ÷ 8 = 1 remainder 4 |
| 5 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 29 | 3944 |
| 123 and 68 | 8364 |
| 114 and 155 | 17670 |
| 161 and 151 | 24311 |
| 12 and 136 | 408 |