LCM and HCF
 How many numbers are there between 4000 and 6000 which are exactly divisible by 32, 40, 48 and 60?

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LCM of 32, 40, 48 and 60 = 480
The number divisible by 480 between 4000 and 6000 are 4320, 4800, 5280 and 5760.Correct Option: C
LCM of 32, 40, 48 and 60 = 480
The number divisible by 480 between 4000 and 6000 are 4320, 4800, 5280 and 5760.
Hence, required number of numbers are 4.
 The sum of two numbers is 1056 and their HCF is 66, Find the Number of such pairs.

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Let the numbers be 66a and 66b, where a and b are coprimes.
According to the question,
66a + 66b = 1056
⇒ 66(a + b) = 1056
⇒ (a + b) = 1056/66 = 16
∴ Possible values of a and b are
(a = 1, b = 15), (a = 3, b = 13).
(a = 5, b = 11 ), (a = 7, b = 9)Correct Option: C
Let the numbers be 66a and 66b, where a and b are coprimes.
According to the question,
66a + 66b = 1056
⇒ 66(a + b) = 1056
⇒ (a + b) = 1056/66 = 16
∴ Possible values of a and b are
(a = 1, b = 15), (a = 3, b = 13).
(a = 5, b = 11 ), (a = 7, b = 9)
∴ Numbers are
(66 x 1, 66 x 15), (66 x 3, 66 x 13),
(66 x 5, 66 x 11), (66 x 7, 66 x 9).
∴ Possible number of pairs = 4
 The HCF and LCM of two natural numbers are 12 and 72, respectively. What is the difference between the two numbers, if one of the number is 24?

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Second number = (LCM x HCF) / first number
Correct Option: A
Second number = (LCM x HCF) / first number
= (72 x 12)/ 24 = 36
Difference between the two numbers
= 36  24 = 12
 The ratio of two numbers is 3 : 4 and their HCF is 4. What will be their LCM?

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According to the question,
1st number = 3M, 2nd number = 4M
where, M = HCF
But given, M = 4
We know that,
LCM = Product of two numbers / HCFCorrect Option: D
According to the question,
1st number = 3M, 2nd number = 4M
where, M = HCF
But given, M = 4
We know that,
LCM = Product of two numbers / HCF
= (3M x 4M) / M
LCM = 12M = 12 x 4 = 48
 For any integer n, What is HCF (22n + 7, 33n + 10) equal to?

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HCF of (22n + 7, 33n + 10) is always 1.
lllustraction
For n = 1, HCF(29, 43) ⇒ HCF = 1
For n = 2, HCF(51, 76) ⇒ HCF = 1
For n = 3, HCF(73, 109) ⇒ HCF = 1Correct Option: B
HCF of (22n + 7, 33n + 10) is always 1.
lllustraction
For n = 1, HCF(29, 43) ⇒ HCF = 1
For n = 2, HCF(51, 76) ⇒ HCF = 1
For n = 3, HCF(73, 109) ⇒ HCF = 1