Least Common Multiple (LCM) of 47 and 60
The least common multiple (LCM) of 47 and 60 is 2820.
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 60?
First, calculate the GCD of 47 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 47 ÷ 60 = 0 remainder 47 |
| 2 | 60 ÷ 47 = 1 remainder 13 |
| 3 | 47 ÷ 13 = 3 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 118 | 11446 |
| 197 and 191 | 37627 |
| 97 and 53 | 5141 |
| 102 and 63 | 2142 |
| 31 and 77 | 2387 |