Least Common Multiple (LCM) of 32 and 169
The least common multiple (LCM) of 32 and 169 is 5408.
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 169?
First, calculate the GCD of 32 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 169 = 0 remainder 32 |
| 2 | 169 ÷ 32 = 5 remainder 9 |
| 3 | 32 ÷ 9 = 3 remainder 5 |
| 4 | 9 ÷ 5 = 1 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 32 | 1632 |
| 190 and 123 | 23370 |
| 200 and 21 | 4200 |
| 57 and 170 | 9690 |
| 114 and 13 | 1482 |