Least Common Multiple (LCM) of 74 and 159
The least common multiple (LCM) of 74 and 159 is 11766.
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 159?
First, calculate the GCD of 74 and 159 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 74 ÷ 159 = 0 remainder 74 |
| 2 | 159 ÷ 74 = 2 remainder 11 |
| 3 | 74 ÷ 11 = 6 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 188 | 24628 |
| 165 and 192 | 10560 |
| 67 and 71 | 4757 |
| 47 and 69 | 3243 |
| 102 and 152 | 7752 |