Least Common Multiple (LCM) of 52 and 176
The least common multiple (LCM) of 52 and 176 is 2288.
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 176?
First, calculate the GCD of 52 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 176 = 0 remainder 52 |
| 2 | 176 ÷ 52 = 3 remainder 20 |
| 3 | 52 ÷ 20 = 2 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 |
|---|---|
| 200 and 105 | 4200 |
| 118 and 112 | 6608 |
| 14 and 138 | 966 |
| 115 and 194 | 22310 |
| 152 and 131 | 19912 |