LCM and HCF
 The smallest number, which when diminished by 3, is divisible by 21, 28, 36 and 45 is ?

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Required number = (L . C . M of 21, 28, 36, 45 ) + 3
Correct Option: D
Required number = (L . C . M of 21, 28, 36, 45 ) + 3
= (1260 + 3 )
= 1263
 The number of prime factors in 2^{222} x 3^{333} x 5^{555} is ?

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The number of prime factors in the given product
= 222 + 333 + 555Correct Option: C
The number of prime factors in the given product
= (222 + 333 + 555)
= 1110.
 The H.C.F and L.C.M of two number are 44 and 264 respectively. If the first number is divided by 2, the quotient is 44. The other number is ?

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First number = 2 x 44 = 88
Second number = (LCM x HCF ) / First numberCorrect Option: C
First number = 2 x 44 = 88
Second number = (LCM x HCF ) / First number
∴ Second number = 44 x 264 / 88 = 132.
 The LCM of two number is 48. The number are in the ratio of 2:3. Find sum of the numbers.

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Let the numbers be 2x and 3x.
So, their LCM = 6x
However, the LCM is given as 48
∴ 6x = 48Correct Option: C
Let the numbers be 2x and 3x.
So, their LCM = 6x
However, the LCM is given as 48
∴ 6x = 48
⇒ x=8
So, the numbers are 16 and 24.
Hence, their sum is 40.
 Find the greatest possible length which can be used to measure 4 m 3 cm, 4 m 34 cm and 4 m 65 cm exactly.

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Required measure = HCF of 403, 434 and 465 = 31 cm
Correct Option: A
Required measure = HCF of 403, 434 and 465 = 31 cm