Least Common Multiple (LCM) of 32 and 117
The least common multiple (LCM) of 32 and 117 is 3744.
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 32 and 117?
First, calculate the GCD of 32 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 117 = 0 remainder 32 |
| 2 | 117 ÷ 32 = 3 remainder 21 |
| 3 | 32 ÷ 21 = 1 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 29 | 377 |
| 62 and 148 | 4588 |
| 107 and 197 | 21079 |
| 173 and 27 | 4671 |
| 161 and 86 | 13846 |