Least Common Multiple (LCM) of 112 and 59
The least common multiple (LCM) of 112 and 59 is 6608.
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 112 and 59?
First, calculate the GCD of 112 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 112 ÷ 59 = 1 remainder 53 |
| 2 | 59 ÷ 53 = 1 remainder 6 |
| 3 | 53 ÷ 6 = 8 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 178 | 5518 |
| 121 and 53 | 6413 |
| 17 and 107 | 1819 |
| 19 and 39 | 741 |
| 72 and 94 | 3384 |