Least Common Multiple (LCM) of 123 and 59
The least common multiple (LCM) of 123 and 59 is 7257.
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 59?
First, calculate the GCD of 123 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 123 ÷ 59 = 2 remainder 5 |
| 2 | 59 ÷ 5 = 11 remainder 4 |
| 3 | 5 ÷ 4 = 1 remainder 1 |
| 4 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 183 and 49 | 8967 |
| 77 and 157 | 12089 |
| 172 and 44 | 1892 |
| 148 and 108 | 3996 |
| 103 and 169 | 17407 |