Least Common Multiple (LCM) of 120 and 70
The least common multiple (LCM) of 120 and 70 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 120 and 70?
First, calculate the GCD of 120 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 70 = 1 remainder 50 |
| 2 | 70 ÷ 50 = 1 remainder 20 |
| 3 | 50 ÷ 20 = 2 remainder 10 |
| 4 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 11 | 1353 |
| 176 and 158 | 13904 |
| 62 and 17 | 1054 |
| 74 and 15 | 1110 |
| 196 and 145 | 28420 |