Least Common Multiple (LCM) of 15 and 49
The least common multiple (LCM) of 15 and 49 is 735.
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 15 and 49?
First, calculate the GCD of 15 and 49 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 49 = 0 remainder 15 |
| 2 | 49 ÷ 15 = 3 remainder 4 |
| 3 | 15 ÷ 4 = 3 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 156 | 4524 |
| 110 and 54 | 2970 |
| 158 and 154 | 12166 |
| 168 and 173 | 29064 |
| 185 and 40 | 1480 |