Least Common Multiple (LCM) of 169 and 45
The least common multiple (LCM) of 169 and 45 is 7605.
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 169 and 45?
First, calculate the GCD of 169 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 45 = 3 remainder 34 |
| 2 | 45 ÷ 34 = 1 remainder 11 |
| 3 | 34 ÷ 11 = 3 remainder 1 |
| 4 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 120 | 3720 |
| 172 and 186 | 15996 |
| 77 and 13 | 1001 |
| 162 and 15 | 810 |
| 53 and 147 | 7791 |