Least Common Multiple (LCM) of 105 and 70
The least common multiple (LCM) of 105 and 70 is 210.
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 105 and 70?
First, calculate the GCD of 105 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 70 = 1 remainder 35 |
| 2 | 70 ÷ 35 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 134 and 196 | 13132 |
| 131 and 196 | 25676 |
| 49 and 168 | 1176 |
| 107 and 59 | 6313 |
| 161 and 128 | 20608 |