Least Common Multiple (LCM) of 71 and 132
The least common multiple (LCM) of 71 and 132 is 9372.
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 71 and 132?
First, calculate the GCD of 71 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 132 = 0 remainder 71 |
| 2 | 132 ÷ 71 = 1 remainder 61 |
| 3 | 71 ÷ 61 = 1 remainder 10 |
| 4 | 61 ÷ 10 = 6 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 35 | 735 |
| 74 and 175 | 12950 |
| 13 and 142 | 1846 |
| 35 and 37 | 1295 |
| 189 and 21 | 189 |