Least Common Multiple (LCM) of 177 and 113
The least common multiple (LCM) of 177 and 113 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 177 and 113?
First, calculate the GCD of 177 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 177 ÷ 113 = 1 remainder 64 |
| 2 | 113 ÷ 64 = 1 remainder 49 |
| 3 | 64 ÷ 49 = 1 remainder 15 |
| 4 | 49 ÷ 15 = 3 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 62 | 1302 |
| 182 and 12 | 1092 |
| 132 and 146 | 9636 |
| 110 and 162 | 8910 |
| 130 and 145 | 3770 |