Least Common Multiple (LCM) of 52 and 188
The least common multiple (LCM) of 52 and 188 is 2444.
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 188?
First, calculate the GCD of 52 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 188 = 0 remainder 52 |
| 2 | 188 ÷ 52 = 3 remainder 32 |
| 3 | 52 ÷ 32 = 1 remainder 20 |
| 4 | 32 ÷ 20 = 1 remainder 12 |
| 5 | 20 ÷ 12 = 1 remainder 8 |
| 6 | 12 ÷ 8 = 1 remainder 4 |
| 7 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 78 | 5694 |
| 17 and 97 | 1649 |
| 165 and 135 | 1485 |
| 112 and 151 | 16912 |
| 70 and 129 | 9030 |