Least Common Multiple (LCM) of 45 and 118
The least common multiple (LCM) of 45 and 118 is 5310.
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 118?
First, calculate the GCD of 45 and 118 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 118 = 0 remainder 45 |
| 2 | 118 ÷ 45 = 2 remainder 28 |
| 3 | 45 ÷ 28 = 1 remainder 17 |
| 4 | 28 ÷ 17 = 1 remainder 11 |
| 5 | 17 ÷ 11 = 1 remainder 6 |
| 6 | 11 ÷ 6 = 1 remainder 5 |
| 7 | 6 ÷ 5 = 1 remainder 1 |
| 8 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 128 | 13952 |
| 28 and 40 | 280 |
| 54 and 131 | 7074 |
| 150 and 43 | 6450 |
| 155 and 92 | 14260 |