Least Common Multiple (LCM) of 154 and 108
The least common multiple (LCM) of 154 and 108 is 8316.
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 154 and 108?
First, calculate the GCD of 154 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 154 ÷ 108 = 1 remainder 46 |
| 2 | 108 ÷ 46 = 2 remainder 16 |
| 3 | 46 ÷ 16 = 2 remainder 14 |
| 4 | 16 ÷ 14 = 1 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 21 | 420 |
| 124 and 45 | 5580 |
| 103 and 75 | 7725 |
| 107 and 184 | 19688 |
| 193 and 102 | 19686 |