Least Common Multiple (LCM) of 47 and 74
The least common multiple (LCM) of 47 and 74 is 3478.
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 47 and 74?
First, calculate the GCD of 47 and 74 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 74 = 0 remainder 47 |
| 2 | 74 ÷ 47 = 1 remainder 27 |
| 3 | 47 ÷ 27 = 1 remainder 20 |
| 4 | 27 ÷ 20 = 1 remainder 7 |
| 5 | 20 ÷ 7 = 2 remainder 6 |
| 6 | 7 ÷ 6 = 1 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 120 | 4440 |
| 151 and 55 | 8305 |
| 180 and 164 | 7380 |
| 150 and 163 | 24450 |
| 108 and 116 | 3132 |