Least Common Multiple (LCM) of 52 and 175
The least common multiple (LCM) of 52 and 175 is 9100.
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 175?
First, calculate the GCD of 52 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 52 ÷ 175 = 0 remainder 52 |
| 2 | 175 ÷ 52 = 3 remainder 19 |
| 3 | 52 ÷ 19 = 2 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 51 and 134 | 6834 |
| 55 and 119 | 6545 |
| 77 and 100 | 7700 |
| 128 and 142 | 9088 |
| 195 and 165 | 2145 |