Least Common Multiple (LCM) of 113 and 176
The least common multiple (LCM) of 113 and 176 is 19888.
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 176?
First, calculate the GCD of 113 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 113 ÷ 176 = 0 remainder 113 |
| 2 | 176 ÷ 113 = 1 remainder 63 |
| 3 | 113 ÷ 63 = 1 remainder 50 |
| 4 | 63 ÷ 50 = 1 remainder 13 |
| 5 | 50 ÷ 13 = 3 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 141 | 5640 |
| 71 and 105 | 7455 |
| 161 and 128 | 20608 |
| 156 and 47 | 7332 |
| 21 and 40 | 840 |