Least Common Multiple (LCM) of 113 and 177
The least common multiple (LCM) of 113 and 177 is 20001.
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 177?
First, calculate the GCD of 113 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 177 = 0 remainder 113 |
| 2 | 177 ÷ 113 = 1 remainder 64 |
| 3 | 113 ÷ 64 = 1 remainder 49 |
| 4 | 64 ÷ 49 = 1 remainder 15 |
| 5 | 49 ÷ 15 = 3 remainder 4 |
| 6 | 15 ÷ 4 = 3 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 56 | 952 |
| 113 and 72 | 8136 |
| 143 and 54 | 7722 |
| 31 and 108 | 3348 |
| 160 and 57 | 9120 |