Least Common Multiple (LCM) of 74 and 90
The least common multiple (LCM) of 74 and 90 is 3330.
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 90?
First, calculate the GCD of 74 and 90 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 90 = 0 remainder 74 |
| 2 | 90 ÷ 74 = 1 remainder 16 |
| 3 | 74 ÷ 16 = 4 remainder 10 |
| 4 | 16 ÷ 10 = 1 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 132 and 182 | 12012 |
| 196 and 192 | 9408 |
| 45 and 148 | 6660 |
| 198 and 142 | 14058 |
| 123 and 92 | 11316 |