Least Common Multiple (LCM) of 45 and 168
The least common multiple (LCM) of 45 and 168 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 45 and 168?
First, calculate the GCD of 45 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 168 = 0 remainder 45 |
| 2 | 168 ÷ 45 = 3 remainder 33 |
| 3 | 45 ÷ 33 = 1 remainder 12 |
| 4 | 33 ÷ 12 = 2 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 140 | 2660 |
| 116 and 67 | 7772 |
| 156 and 178 | 13884 |
| 80 and 129 | 10320 |
| 40 and 78 | 1560 |