Least Common Multiple (LCM) of 107 and 23
The least common multiple (LCM) of 107 and 23 is 2461.
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 107 and 23?
First, calculate the GCD of 107 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 23 = 4 remainder 15 |
| 2 | 23 ÷ 15 = 1 remainder 8 |
| 3 | 15 ÷ 8 = 1 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 18 | 1656 |
| 164 and 75 | 12300 |
| 170 and 139 | 23630 |
| 173 and 32 | 5536 |
| 148 and 21 | 3108 |