Least Common Multiple (LCM) of 188 and 52
The least common multiple (LCM) of 188 and 52 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 188 and 52?
First, calculate the GCD of 188 and 52 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 52 = 3 remainder 32 |
| 2 | 52 ÷ 32 = 1 remainder 20 |
| 3 | 32 ÷ 20 = 1 remainder 12 |
| 4 | 20 ÷ 12 = 1 remainder 8 |
| 5 | 12 ÷ 8 = 1 remainder 4 |
| 6 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 155 | 6045 |
| 140 and 190 | 2660 |
| 145 and 52 | 7540 |
| 150 and 36 | 900 |
| 49 and 109 | 5341 |