Least Common Multiple (LCM) of 100 and 77
The least common multiple (LCM) of 100 and 77 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 100 and 77?
First, calculate the GCD of 100 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 77 = 1 remainder 23 |
| 2 | 77 ÷ 23 = 3 remainder 8 |
| 3 | 23 ÷ 8 = 2 remainder 7 |
| 4 | 8 ÷ 7 = 1 remainder 1 |
| 5 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 40 | 2760 |
| 48 and 192 | 192 |
| 150 and 48 | 1200 |
| 184 and 75 | 13800 |
| 103 and 120 | 12360 |