Least Common Multiple (LCM) of 178 and 98
The least common multiple (LCM) of 178 and 98 is 8722.
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 178 and 98?
First, calculate the GCD of 178 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 98 = 1 remainder 80 |
| 2 | 98 ÷ 80 = 1 remainder 18 |
| 3 | 80 ÷ 18 = 4 remainder 8 |
| 4 | 18 ÷ 8 = 2 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 106 | 11554 |
| 87 and 142 | 12354 |
| 161 and 12 | 1932 |
| 100 and 51 | 5100 |
| 151 and 170 | 25670 |