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The HCF of two numbers is 16 and their product is 3072. What is the LCM?
- a)182
- b)162
- c)192
- d)196
Correct answer is option 'C'. Can you explain this answer?
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The HCF of two numbers is 16 and their product is 3072. What is the LC...
HCF x LCM = ab
16 x LCM = 3072
LCM = 3072 / 16
= 192
So, the LCM of the two number is 192
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The HCF of two numbers is 16 and their product is 3072. What is the LC...
Given information:
- HCF of two numbers = 16
- Product of two numbers = 3072
Finding the two numbers:
Let the two numbers be a and b.
Given that HCF(a, b) = 16, we can write the two numbers as:
a = 16x
b = 16y
where x and y are co-prime numbers.
The product of the two numbers is given as 3072:
16x * 16y = 3072
256xy = 3072
xy = 12
So, the possible values of x and y could be:
x = 1, y = 12
x = 2, y = 6
x = 3, y = 4
Therefore, the two numbers could be:
a = 16 * 1 = 16, b = 16 * 12 = 192
a = 16 * 2 = 32, b = 16 * 6 = 96
a = 16 * 3 = 48, b = 16 * 4 = 64
Calculating the LCM:
To find the LCM of two numbers, we can use the formula:
LCM(a, b) = (a * b) / HCF(a, b)
Substitute the values of a, b, and HCF in the formula:
LCM(16, 192) = (16 * 192) / 16
LCM(16, 192) = 3072 / 16
LCM(16, 192) = 192
Therefore, the LCM of the two numbers is 192, which corresponds to option 'c'.
- HCF of two numbers = 16
- Product of two numbers = 3072
Finding the two numbers:
Let the two numbers be a and b.
Given that HCF(a, b) = 16, we can write the two numbers as:
a = 16x
b = 16y
where x and y are co-prime numbers.
The product of the two numbers is given as 3072:
16x * 16y = 3072
256xy = 3072
xy = 12
So, the possible values of x and y could be:
x = 1, y = 12
x = 2, y = 6
x = 3, y = 4
Therefore, the two numbers could be:
a = 16 * 1 = 16, b = 16 * 12 = 192
a = 16 * 2 = 32, b = 16 * 6 = 96
a = 16 * 3 = 48, b = 16 * 4 = 64
Calculating the LCM:
To find the LCM of two numbers, we can use the formula:
LCM(a, b) = (a * b) / HCF(a, b)
Substitute the values of a, b, and HCF in the formula:
LCM(16, 192) = (16 * 192) / 16
LCM(16, 192) = 3072 / 16
LCM(16, 192) = 192
Therefore, the LCM of the two numbers is 192, which corresponds to option 'c'.
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The HCF of two numbers is 16 and their product is 3072. What is the LC...
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The HCF of two numbers is 16 and their product is 3072. What is the LCM?a)182b)162c)192d)196Correct answer is option 'C'. Can you explain this answer?
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