Least Common Multiple (LCM) of 136 and 177
The least common multiple (LCM) of 136 and 177 is 24072.
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 136 and 177?
First, calculate the GCD of 136 and 177 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 177 = 0 remainder 136 |
| 2 | 177 ÷ 136 = 1 remainder 41 |
| 3 | 136 ÷ 41 = 3 remainder 13 |
| 4 | 41 ÷ 13 = 3 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 77 | 154 |
| 11 and 104 | 1144 |
| 128 and 72 | 1152 |
| 172 and 72 | 3096 |
| 75 and 148 | 11100 |