Find two natural numbers in ratio 5:7 such that their lives. L C.m. is 210
210 = 5*7*3
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sorry.
210 = 5*7 * 2*3
30 and 42
To find two natural numbers in the ratio 5:7, we can use the concept of proportion.
Let's assume the two natural numbers are 5x and 7x, where x is a common factor.
According to the problem, their least common multiple (LCM) is 210. This means that the smallest number that is divisible by both 5x and 7x is 210.
To find the LCM, we need to find the highest power of each prime factor in the two numbers' prime factorization.
Prime factorization of 5x:
5x = 5 * x
Prime factorization of 7x:
7x = 7 * x
The LCM of 5x and 7x will include the highest powers of each prime factor (5 and 7) from their factorizations. Therefore, the LCM is 5 * 7 * x = 35x.
We know that the LCM is 210. So, we can equate 35x to 210 and solve for x:
35x = 210
Divide both sides by 35:
x = 210 / 35
x = 6
Now that we have the value of x, we can calculate the two natural numbers:
First number = 5x = 5 * 6 = 30
Second number = 7x = 7 * 6 = 42
Therefore, the two natural numbers in the ratio 5:7, with a least common multiple of 210, are 30 and 42.