Least Common Multiple (LCM) of 45 and 114
The least common multiple (LCM) of 45 and 114 is 1710.
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 114?
First, calculate the GCD of 45 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 114 = 0 remainder 45 |
| 2 | 114 ÷ 45 = 2 remainder 24 |
| 3 | 45 ÷ 24 = 1 remainder 21 |
| 4 | 24 ÷ 21 = 1 remainder 3 |
| 5 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 77 | 462 |
| 76 and 69 | 5244 |
| 123 and 41 | 123 |
| 11 and 175 | 1925 |
| 105 and 37 | 3885 |