Least Common Multiple (LCM) of 77 and 23
The least common multiple (LCM) of 77 and 23 is 1771.
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 23?
First, calculate the GCD of 77 and 23 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 23 = 3 remainder 8 |
| 2 | 23 ÷ 8 = 2 remainder 7 |
| 3 | 8 ÷ 7 = 1 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 171 | 1197 |
| 32 and 160 | 160 |
| 170 and 31 | 5270 |
| 113 and 40 | 4520 |
| 16 and 142 | 1136 |