Least Common Multiple (LCM) of 123 and 13
The least common multiple (LCM) of 123 and 13 is 1599.
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 13?
First, calculate the GCD of 123 and 13 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 13 = 9 remainder 6 |
| 2 | 13 ÷ 6 = 2 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 50 | 8450 |
| 19 and 112 | 2128 |
| 59 and 51 | 3009 |
| 24 and 105 | 840 |
| 103 and 154 | 15862 |