Least Common Multiple (LCM) of 133 and 77
The least common multiple (LCM) of 133 and 77 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 133 and 77?
First, calculate the GCD of 133 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 133 ÷ 77 = 1 remainder 56 |
| 2 | 77 ÷ 56 = 1 remainder 21 |
| 3 | 56 ÷ 21 = 2 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 107 | 3852 |
| 142 and 12 | 852 |
| 78 and 152 | 5928 |
| 137 and 108 | 14796 |
| 170 and 115 | 3910 |