Least Common Multiple (LCM) of 132 and 76
The least common multiple (LCM) of 132 and 76 is 2508.
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 132 and 76?
First, calculate the GCD of 132 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 76 = 1 remainder 56 |
| 2 | 76 ÷ 56 = 1 remainder 20 |
| 3 | 56 ÷ 20 = 2 remainder 16 |
| 4 | 20 ÷ 16 = 1 remainder 4 |
| 5 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 86 | 4988 |
| 117 and 77 | 9009 |
| 19 and 126 | 2394 |
| 34 and 85 | 170 |
| 103 and 54 | 5562 |