Least Common Multiple (LCM) of 55 and 98
The least common multiple (LCM) of 55 and 98 is 5390.
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 55 and 98?
First, calculate the GCD of 55 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 55 ÷ 98 = 0 remainder 55 |
| 2 | 98 ÷ 55 = 1 remainder 43 |
| 3 | 55 ÷ 43 = 1 remainder 12 |
| 4 | 43 ÷ 12 = 3 remainder 7 |
| 5 | 12 ÷ 7 = 1 remainder 5 |
| 6 | 7 ÷ 5 = 1 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 126 | 1638 |
| 110 and 21 | 2310 |
| 131 and 64 | 8384 |
| 79 and 96 | 7584 |
| 76 and 137 | 10412 |