Least Common Multiple (LCM) of 77 and 136
The least common multiple (LCM) of 77 and 136 is 10472.
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 77 and 136?
First, calculate the GCD of 77 and 136 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 136 = 0 remainder 77 |
| 2 | 136 ÷ 77 = 1 remainder 59 |
| 3 | 77 ÷ 59 = 1 remainder 18 |
| 4 | 59 ÷ 18 = 3 remainder 5 |
| 5 | 18 ÷ 5 = 3 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 164 and 159 | 26076 |
| 183 and 180 | 10980 |
| 182 and 160 | 14560 |
| 112 and 136 | 1904 |
| 10 and 45 | 90 |