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 |
|---|---|
| 92 and 114 | 5244 |
| 126 and 134 | 8442 |
| 140 and 73 | 10220 |
| 57 and 162 | 3078 |
| 140 and 70 | 140 |