Least Common Multiple (LCM) of 77 and 133
The least common multiple (LCM) of 77 and 133 is 1463.
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 133?
First, calculate the GCD of 77 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 133 = 0 remainder 77 |
| 2 | 133 ÷ 77 = 1 remainder 56 |
| 3 | 77 ÷ 56 = 1 remainder 21 |
| 4 | 56 ÷ 21 = 2 remainder 14 |
| 5 | 21 ÷ 14 = 1 remainder 7 |
| 6 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 35 | 4515 |
| 125 and 178 | 22250 |
| 38 and 122 | 2318 |
| 138 and 10 | 690 |
| 177 and 139 | 24603 |