Least Common Multiple (LCM) of 53 and 188
The least common multiple (LCM) of 53 and 188 is 9964.
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 53 and 188?
First, calculate the GCD of 53 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 188 = 0 remainder 53 |
| 2 | 188 ÷ 53 = 3 remainder 29 |
| 3 | 53 ÷ 29 = 1 remainder 24 |
| 4 | 29 ÷ 24 = 1 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 110 | 15070 |
| 92 and 186 | 8556 |
| 167 and 62 | 10354 |
| 176 and 100 | 4400 |
| 97 and 197 | 19109 |