Least Common Multiple (LCM) of 45 and 62
The least common multiple (LCM) of 45 and 62 is 2790.
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 62?
First, calculate the GCD of 45 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 62 = 0 remainder 45 |
| 2 | 62 ÷ 45 = 1 remainder 17 |
| 3 | 45 ÷ 17 = 2 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 185 and 65 | 2405 |
| 149 and 185 | 27565 |
| 28 and 27 | 756 |
| 173 and 175 | 30275 |
| 150 and 171 | 8550 |