Least Common Multiple (LCM) of 113 and 59
The least common multiple (LCM) of 113 and 59 is 6667.
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 113 and 59?
First, calculate the GCD of 113 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 59 = 1 remainder 54 |
| 2 | 59 ÷ 54 = 1 remainder 5 |
| 3 | 54 ÷ 5 = 10 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 177 and 39 | 2301 |
| 54 and 152 | 4104 |
| 13 and 121 | 1573 |
| 118 and 89 | 10502 |
| 128 and 58 | 3712 |