Least Common Multiple (LCM) of 15 and 35
The least common multiple (LCM) of 15 and 35 is 105.
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 35?
First, calculate the GCD of 15 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 35 = 0 remainder 15 |
| 2 | 35 ÷ 15 = 2 remainder 5 |
| 3 | 15 ÷ 5 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 181 | 24978 |
| 115 and 22 | 2530 |
| 190 and 59 | 11210 |
| 120 and 164 | 4920 |
| 80 and 147 | 11760 |