Least Common Multiple (LCM) of 45 and 98
The least common multiple (LCM) of 45 and 98 is 4410.
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 45 and 98?
First, calculate the GCD of 45 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 98 = 0 remainder 45 |
| 2 | 98 ÷ 45 = 2 remainder 8 |
| 3 | 45 ÷ 8 = 5 remainder 5 |
| 4 | 8 ÷ 5 = 1 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 200 and 60 | 600 |
| 188 and 21 | 3948 |
| 47 and 21 | 987 |
| 194 and 133 | 25802 |
| 181 and 159 | 28779 |