Least Common Multiple (LCM) of 172 and 53
The least common multiple (LCM) of 172 and 53 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 172 and 53?
First, calculate the GCD of 172 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 53 = 3 remainder 13 |
| 2 | 53 ÷ 13 = 4 remainder 1 |
| 3 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 64 | 1728 |
| 127 and 192 | 24384 |
| 65 and 165 | 2145 |
| 189 and 119 | 3213 |
| 19 and 78 | 1482 |