Least Common Multiple (LCM) of 77 and 100
The least common multiple (LCM) of 77 and 100 is 7700.
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 100?
First, calculate the GCD of 77 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 100 = 0 remainder 77 |
| 2 | 100 ÷ 77 = 1 remainder 23 |
| 3 | 77 ÷ 23 = 3 remainder 8 |
| 4 | 23 ÷ 8 = 2 remainder 7 |
| 5 | 8 ÷ 7 = 1 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 113 | 19436 |
| 101 and 137 | 13837 |
| 148 and 35 | 5180 |
| 194 and 23 | 4462 |
| 107 and 74 | 7918 |