Least Common Multiple (LCM) of 52 and 132
The least common multiple (LCM) of 52 and 132 is 1716.
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 52 and 132?
First, calculate the GCD of 52 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 132 = 0 remainder 52 |
| 2 | 132 ÷ 52 = 2 remainder 28 |
| 3 | 52 ÷ 28 = 1 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 77 and 66 | 462 |
| 10 and 188 | 940 |
| 83 and 174 | 14442 |
| 141 and 10 | 1410 |
| 27 and 65 | 1755 |