Least Common Multiple (LCM) of 52 and 133
The least common multiple (LCM) of 52 and 133 is 6916.
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 133?
First, calculate the GCD of 52 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 133 = 0 remainder 52 |
| 2 | 133 ÷ 52 = 2 remainder 29 |
| 3 | 52 ÷ 29 = 1 remainder 23 |
| 4 | 29 ÷ 23 = 1 remainder 6 |
| 5 | 23 ÷ 6 = 3 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 155 and 139 | 21545 |
| 24 and 84 | 168 |
| 110 and 112 | 6160 |
| 122 and 88 | 5368 |
| 97 and 132 | 12804 |