Least Common Multiple (LCM) of 68 and 124
The least common multiple (LCM) of 68 and 124 is 2108.
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 68 and 124?
First, calculate the GCD of 68 and 124 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 68 ÷ 124 = 0 remainder 68 |
| 2 | 124 ÷ 68 = 1 remainder 56 |
| 3 | 68 ÷ 56 = 1 remainder 12 |
| 4 | 56 ÷ 12 = 4 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 169 | 23660 |
| 111 and 95 | 10545 |
| 100 and 188 | 4700 |
| 127 and 143 | 18161 |
| 37 and 84 | 3108 |