Least Common Multiple (LCM) of 65 and 172
The least common multiple (LCM) of 65 and 172 is 11180.
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 65 and 172?
First, calculate the GCD of 65 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 172 = 0 remainder 65 |
| 2 | 172 ÷ 65 = 2 remainder 42 |
| 3 | 65 ÷ 42 = 1 remainder 23 |
| 4 | 42 ÷ 23 = 1 remainder 19 |
| 5 | 23 ÷ 19 = 1 remainder 4 |
| 6 | 19 ÷ 4 = 4 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 69 | 12765 |
| 111 and 67 | 7437 |
| 175 and 118 | 20650 |
| 150 and 134 | 10050 |
| 141 and 21 | 987 |