Least Common Multiple (LCM) of 53 and 172
The least common multiple (LCM) of 53 and 172 is 9116.
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 172?
First, calculate the GCD of 53 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 172 = 0 remainder 53 |
| 2 | 172 ÷ 53 = 3 remainder 13 |
| 3 | 53 ÷ 13 = 4 remainder 1 |
| 4 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 133 | 21546 |
| 117 and 125 | 14625 |
| 57 and 140 | 7980 |
| 13 and 180 | 2340 |
| 105 and 11 | 1155 |