Least Common Multiple (LCM) of 46 and 99
The least common multiple (LCM) of 46 and 99 is 4554.
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 46 and 99?
First, calculate the GCD of 46 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 99 = 0 remainder 46 |
| 2 | 99 ÷ 46 = 2 remainder 7 |
| 3 | 46 ÷ 7 = 6 remainder 4 |
| 4 | 7 ÷ 4 = 1 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 198 | 3762 |
| 10 and 38 | 190 |
| 129 and 149 | 19221 |
| 181 and 112 | 20272 |
| 114 and 14 | 798 |