Least Common Multiple (LCM) of 42 and 74
The least common multiple (LCM) of 42 and 74 is 1554.
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 42 and 74?
First, calculate the GCD of 42 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 74 = 0 remainder 42 |
| 2 | 74 ÷ 42 = 1 remainder 32 |
| 3 | 42 ÷ 32 = 1 remainder 10 |
| 4 | 32 ÷ 10 = 3 remainder 2 |
| 5 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 121 | 121 |
| 101 and 60 | 6060 |
| 22 and 154 | 154 |
| 165 and 130 | 4290 |
| 123 and 70 | 8610 |