Least Common Multiple (LCM) of 77 and 98
The least common multiple (LCM) of 77 and 98 is 1078.
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 98?
First, calculate the GCD of 77 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 98 = 0 remainder 77 |
| 2 | 98 ÷ 77 = 1 remainder 21 |
| 3 | 77 ÷ 21 = 3 remainder 14 |
| 4 | 21 ÷ 14 = 1 remainder 7 |
| 5 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 123 | 7380 |
| 117 and 44 | 5148 |
| 176 and 125 | 22000 |
| 188 and 168 | 7896 |
| 137 and 71 | 9727 |