Least Common Multiple (LCM) of 70 and 119
The least common multiple (LCM) of 70 and 119 is 1190.
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 119?
First, calculate the GCD of 70 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 119 = 0 remainder 70 |
| 2 | 119 ÷ 70 = 1 remainder 49 |
| 3 | 70 ÷ 49 = 1 remainder 21 |
| 4 | 49 ÷ 21 = 2 remainder 7 |
| 5 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 156 | 1248 |
| 158 and 54 | 4266 |
| 157 and 192 | 30144 |
| 137 and 112 | 15344 |
| 51 and 170 | 510 |