Least Common Multiple (LCM) of 70 and 192
The least common multiple (LCM) of 70 and 192 is 6720.
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 192?
First, calculate the GCD of 70 and 192 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 192 = 0 remainder 70 |
| 2 | 192 ÷ 70 = 2 remainder 52 |
| 3 | 70 ÷ 52 = 1 remainder 18 |
| 4 | 52 ÷ 18 = 2 remainder 16 |
| 5 | 18 ÷ 16 = 1 remainder 2 |
| 6 | 16 ÷ 2 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 69 | 6072 |
| 50 and 103 | 5150 |
| 45 and 89 | 4005 |
| 84 and 145 | 12180 |
| 178 and 153 | 27234 |