Least Common Multiple (LCM) of 70 and 12
The least common multiple (LCM) of 70 and 12 is 420.
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 70 and 12?
First, calculate the GCD of 70 and 12 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 12 = 5 remainder 10 |
| 2 | 12 ÷ 10 = 1 remainder 2 |
| 3 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 164 | 22140 |
| 123 and 178 | 21894 |
| 67 and 129 | 8643 |
| 176 and 46 | 4048 |
| 139 and 141 | 19599 |