1.
The L.C.M. of two numbers is 45 times their H.C.F. If one of the numbers is 125 and the sum of H.C.F. and L.C.M. is 1150, the other number is:
• A.
215
• C.
225
• B.
220
• D.
235
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Explanation :

Let H.C.F. be h and L.C.M. be I

Then, I =45h and I + h = 1150.

 45h + h = 1150 or h = 25.

So, I = (1150 - 25) = 1125.

 Hence, other number = 25 x 1125 = 225. 125

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2.
H.C.F. of 3240, 3600 and a third number is 36 and their L.C.M. is 24 x 35 x 52 x 72
The third number is:
• A.
22 x 35 x 72
• C.
25 x 52 x 72
• B.
22 x 53 x 72
• D.
23 x 35 x 72
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Explanation :

3240 = 23 x 34 x 5; 3600 = 24 x 32 x 52; H.C.F. = 36 = 22 x 32

Since H.C.F. is the product of lowest powers of common factors,

so the third number must have (22 x 32) as its factors

Since L.C.M. is the product of highest powers of common prime factors,

so the third number must have 35 and 72 as its factors.

 Third number = 22 x 35 x 72

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3.
 Four different electronic devices make a beep after every 30 minutes, 1 hour, 1 1 hour 2
and 1 hour 45 minutes respectively. All the devices beeped together at 12 noon. They
will again beep together at:
• A.
12 midnight
• C.
6 a.m.
• B.
3 a.m.
• D.
9 a.m.
• Report
Explanation :

Interval after which the devices will beep together = (L.C.M. of 30, 60, 90, 105) min.

 = 1260 min.

 = 21 hrs.

So, the devices will again beep together 21 hrs. after 12 noon i.e., at 9 a.m.

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4.
The H.C.F of 204, 1190 and 1445 is:
• A.
17
• C.
19
• B.
18
• D.
21
• Report
Explanation :

204 = 22 x 3 x 17; 1190 = 2 x 5 x 7 x 17; 1445 = 5 x 172

 H.C.F. = 17

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5.
 The H.C.F. of 2 , 8 , 64 and 10 is: 3 9 81 27
•  A. 2 3
•  C. 160 3
•  B. 2 81
•  D. 160 81