Least Common Multiple (LCM) of 27 and 98
The least common multiple (LCM) of 27 and 98 is 2646.
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 27 and 98?
First, calculate the GCD of 27 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 27 ÷ 98 = 0 remainder 27 |
| 2 | 98 ÷ 27 = 3 remainder 17 |
| 3 | 27 ÷ 17 = 1 remainder 10 |
| 4 | 17 ÷ 10 = 1 remainder 7 |
| 5 | 10 ÷ 7 = 1 remainder 3 |
| 6 | 7 ÷ 3 = 2 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 195 | 6630 |
| 144 and 106 | 7632 |
| 80 and 32 | 160 |
| 158 and 120 | 9480 |
| 189 and 29 | 5481 |