Least Common Multiple (LCM) of 70 and 120
The least common multiple (LCM) of 70 and 120 is 840.
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 120?
First, calculate the GCD of 70 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 120 = 0 remainder 70 |
| 2 | 120 ÷ 70 = 1 remainder 50 |
| 3 | 70 ÷ 50 = 1 remainder 20 |
| 4 | 50 ÷ 20 = 2 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 192 and 113 | 21696 |
| 69 and 77 | 5313 |
| 33 and 156 | 1716 |
| 46 and 176 | 4048 |
| 10 and 94 | 470 |