Least Common Multiple (LCM) of 98 and 111
The least common multiple (LCM) of 98 and 111 is 10878.
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 98 and 111?
First, calculate the GCD of 98 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 98 ÷ 111 = 0 remainder 98 |
| 2 | 111 ÷ 98 = 1 remainder 13 |
| 3 | 98 ÷ 13 = 7 remainder 7 |
| 4 | 13 ÷ 7 = 1 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 60 | 10140 |
| 162 and 38 | 3078 |
| 153 and 83 | 12699 |
| 117 and 152 | 17784 |
| 142 and 37 | 5254 |