Least Common Multiple (LCM) of 45 and 169
The least common multiple (LCM) of 45 and 169 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 45 and 169?
First, calculate the GCD of 45 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 169 = 0 remainder 45 |
| 2 | 169 ÷ 45 = 3 remainder 34 |
| 3 | 45 ÷ 34 = 1 remainder 11 |
| 4 | 34 ÷ 11 = 3 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 33 and 125 | 4125 |
| 104 and 54 | 2808 |
| 95 and 137 | 13015 |
| 111 and 61 | 6771 |
| 169 and 117 | 1521 |