Least Common Multiple (LCM) of 132 and 74
The least common multiple (LCM) of 132 and 74 is 4884.
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 74?
First, calculate the GCD of 132 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 132 ÷ 74 = 1 remainder 58 |
| 2 | 74 ÷ 58 = 1 remainder 16 |
| 3 | 58 ÷ 16 = 3 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 107 | 7490 |
| 182 and 141 | 25662 |
| 178 and 199 | 35422 |
| 16 and 188 | 752 |
| 182 and 26 | 182 |