Least Common Multiple (LCM) of 40 and 99
The least common multiple (LCM) of 40 and 99 is 3960.
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 40 and 99?
First, calculate the GCD of 40 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 40 ÷ 99 = 0 remainder 40 |
| 2 | 99 ÷ 40 = 2 remainder 19 |
| 3 | 40 ÷ 19 = 2 remainder 2 |
| 4 | 19 ÷ 2 = 9 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 186 | 10974 |
| 60 and 110 | 660 |
| 124 and 147 | 18228 |
| 183 and 167 | 30561 |
| 148 and 188 | 6956 |