Least Common Multiple (LCM) of 16 and 70
The least common multiple (LCM) of 16 and 70 is 560.
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 16 and 70?
First, calculate the GCD of 16 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 16 ÷ 70 = 0 remainder 16 |
| 2 | 70 ÷ 16 = 4 remainder 6 |
| 3 | 16 ÷ 6 = 2 remainder 4 |
| 4 | 6 ÷ 4 = 1 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 186 | 20274 |
| 73 and 50 | 3650 |
| 186 and 34 | 3162 |
| 136 and 96 | 1632 |
| 21 and 129 | 903 |