Least Common Multiple (LCM) of 40 and 77
The least common multiple (LCM) of 40 and 77 is 3080.
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 40 and 77?
First, calculate the GCD of 40 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 77 = 0 remainder 40 |
| 2 | 77 ÷ 40 = 1 remainder 37 |
| 3 | 40 ÷ 37 = 1 remainder 3 |
| 4 | 37 ÷ 3 = 12 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 137 | 2877 |
| 160 and 164 | 6560 |
| 67 and 96 | 6432 |
| 67 and 146 | 9782 |
| 15 and 182 | 2730 |