Least Common Multiple (LCM) of 74 and 135
The least common multiple (LCM) of 74 and 135 is 9990.
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 74 and 135?
First, calculate the GCD of 74 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 135 = 0 remainder 74 |
| 2 | 135 ÷ 74 = 1 remainder 61 |
| 3 | 74 ÷ 61 = 1 remainder 13 |
| 4 | 61 ÷ 13 = 4 remainder 9 |
| 5 | 13 ÷ 9 = 1 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 48 and 67 | 3216 |
| 105 and 171 | 5985 |
| 45 and 19 | 855 |
| 13 and 150 | 1950 |
| 167 and 89 | 14863 |