Least Common Multiple (LCM) of 59 and 108
The least common multiple (LCM) of 59 and 108 is 6372.
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 59 and 108?
First, calculate the GCD of 59 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 108 = 0 remainder 59 |
| 2 | 108 ÷ 59 = 1 remainder 49 |
| 3 | 59 ÷ 49 = 1 remainder 10 |
| 4 | 49 ÷ 10 = 4 remainder 9 |
| 5 | 10 ÷ 9 = 1 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 184 and 49 | 9016 |
| 141 and 142 | 20022 |
| 125 and 101 | 12625 |
| 73 and 79 | 5767 |
| 52 and 16 | 208 |