Least Common Multiple (LCM) of 14 and 35
The least common multiple (LCM) of 14 and 35 is 70.
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 14 and 35?
First, calculate the GCD of 14 and 35 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 14 ÷ 35 = 0 remainder 14 |
| 2 | 35 ÷ 14 = 2 remainder 7 |
| 3 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 23 | 3450 |
| 176 and 101 | 17776 |
| 60 and 48 | 240 |
| 86 and 64 | 2752 |
| 116 and 43 | 4988 |