Least Common Multiple (LCM) of 47 and 132
The least common multiple (LCM) of 47 and 132 is 6204.
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 47 and 132?
First, calculate the GCD of 47 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 132 = 0 remainder 47 |
| 2 | 132 ÷ 47 = 2 remainder 38 |
| 3 | 47 ÷ 38 = 1 remainder 9 |
| 4 | 38 ÷ 9 = 4 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 200 | 600 |
| 32 and 71 | 2272 |
| 146 and 48 | 3504 |
| 88 and 140 | 3080 |
| 118 and 181 | 21358 |