Least Common Multiple (LCM) of 43 and 98
The least common multiple (LCM) of 43 and 98 is 4214.
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 43 and 98?
First, calculate the GCD of 43 and 98 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 43 ÷ 98 = 0 remainder 43 |
| 2 | 98 ÷ 43 = 2 remainder 12 |
| 3 | 43 ÷ 12 = 3 remainder 7 |
| 4 | 12 ÷ 7 = 1 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 121 and 166 | 20086 |
| 20 and 189 | 3780 |
| 122 and 99 | 12078 |
| 132 and 141 | 6204 |
| 103 and 145 | 14935 |