Answer:
To find the least positive value of b, we need to use the formula for the least common multiple (LCM) of two numbers, which states that:
LCM(a, b) = (a * b) / GCD(a, b)
Given that LCM(a, b) = 20160 and a = 60, we can substitute these values into the formula:
20160 = (60 * b) / GCD(60, b)
To find the least positive value of b, we need to determine the greatest common divisor (GCD) of 60 and b. Since 60 is a multiple of 2^2 and 3^1, the GCD(60, b) must also contain the same prime factors.
The prime factorization of 20160 is 2^7 * 3^2 * 5 * 7. To make LCM(a, b) equal to 20160, b needs to contain the missing prime factors and their corresponding exponents.
Therefore, the least positive value of b is:
b = 2^5 * 3^1 * 5^1 * 7^1 = 20160 / 60 = 336