Least Common Multiple (LCM) of 75 and 98
The least common multiple (LCM) of 75 and 98 is 7350.
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 75 and 98?
First, calculate the GCD of 75 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 98 = 0 remainder 75 |
| 2 | 98 ÷ 75 = 1 remainder 23 |
| 3 | 75 ÷ 23 = 3 remainder 6 |
| 4 | 23 ÷ 6 = 3 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 76 | 2584 |
| 137 and 53 | 7261 |
| 10 and 91 | 910 |
| 163 and 47 | 7661 |
| 81 and 16 | 1296 |