Least Common Multiple (LCM) of 45 and 167
The least common multiple (LCM) of 45 and 167 is 7515.
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 167?
First, calculate the GCD of 45 and 167 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 167 = 0 remainder 45 |
| 2 | 167 ÷ 45 = 3 remainder 32 |
| 3 | 45 ÷ 32 = 1 remainder 13 |
| 4 | 32 ÷ 13 = 2 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 68 | 1292 |
| 40 and 17 | 680 |
| 177 and 46 | 8142 |
| 130 and 171 | 22230 |
| 113 and 113 | 113 |