Least Common Multiple (LCM) of 45 and 76
The least common multiple (LCM) of 45 and 76 is 3420.
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 76?
First, calculate the GCD of 45 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 76 = 0 remainder 45 |
| 2 | 76 ÷ 45 = 1 remainder 31 |
| 3 | 45 ÷ 31 = 1 remainder 14 |
| 4 | 31 ÷ 14 = 2 remainder 3 |
| 5 | 14 ÷ 3 = 4 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 173 | 31486 |
| 197 and 113 | 22261 |
| 198 and 19 | 3762 |
| 175 and 16 | 2800 |
| 107 and 131 | 14017 |