Least Common Multiple (LCM) of 77 and 40
The least common multiple (LCM) of 77 and 40 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 77 and 40?
First, calculate the GCD of 77 and 40 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 40 = 1 remainder 37 |
| 2 | 40 ÷ 37 = 1 remainder 3 |
| 3 | 37 ÷ 3 = 12 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 123 | 13776 |
| 44 and 123 | 5412 |
| 169 and 46 | 7774 |
| 112 and 141 | 15792 |
| 120 and 98 | 5880 |