Least Common Multiple (LCM) of 168 and 45
The least common multiple (LCM) of 168 and 45 is 2520.
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 168 and 45?
First, calculate the GCD of 168 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 168 ÷ 45 = 3 remainder 33 |
| 2 | 45 ÷ 33 = 1 remainder 12 |
| 3 | 33 ÷ 12 = 2 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 119 | 3689 |
| 123 and 167 | 20541 |
| 49 and 184 | 9016 |
| 27 and 122 | 3294 |
| 112 and 99 | 11088 |