Least Common Multiple (LCM) of 77 and 134
The least common multiple (LCM) of 77 and 134 is 10318.
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 134?
First, calculate the GCD of 77 and 134 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 134 = 0 remainder 77 |
| 2 | 134 ÷ 77 = 1 remainder 57 |
| 3 | 77 ÷ 57 = 1 remainder 20 |
| 4 | 57 ÷ 20 = 2 remainder 17 |
| 5 | 20 ÷ 17 = 1 remainder 3 |
| 6 | 17 ÷ 3 = 5 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 106 | 9010 |
| 199 and 20 | 3980 |
| 149 and 34 | 5066 |
| 132 and 131 | 17292 |
| 138 and 86 | 5934 |