Least Common Multiple (LCM) of 45 and 77
The least common multiple (LCM) of 45 and 77 is 3465.
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 77?
First, calculate the GCD of 45 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 77 = 0 remainder 45 |
| 2 | 77 ÷ 45 = 1 remainder 32 |
| 3 | 45 ÷ 32 = 1 remainder 13 |
| 4 | 32 ÷ 13 = 2 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 90 | 8820 |
| 49 and 135 | 6615 |
| 10 and 17 | 170 |
| 41 and 37 | 1517 |
| 47 and 42 | 1974 |