Least Common Multiple (LCM) of 49 and 74
The least common multiple (LCM) of 49 and 74 is 3626.
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 49 and 74?
First, calculate the GCD of 49 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 74 = 0 remainder 49 |
| 2 | 74 ÷ 49 = 1 remainder 25 |
| 3 | 49 ÷ 25 = 1 remainder 24 |
| 4 | 25 ÷ 24 = 1 remainder 1 |
| 5 | 24 ÷ 1 = 24 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 149 | 15347 |
| 43 and 160 | 6880 |
| 133 and 128 | 17024 |
| 120 and 102 | 2040 |
| 95 and 147 | 13965 |