Least Common Multiple (LCM) of 123 and 17
The least common multiple (LCM) of 123 and 17 is 2091.
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 123 and 17?
First, calculate the GCD of 123 and 17 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 17 = 7 remainder 4 |
| 2 | 17 ÷ 4 = 4 remainder 1 |
| 3 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 114 and 62 | 3534 |
| 98 and 160 | 7840 |
| 116 and 182 | 10556 |
| 125 and 99 | 12375 |
| 105 and 40 | 840 |