LCM and HCF
- What least number must be subtracted from 1294 so that the remainder when divided by 9, 11,13 will leave in each case the same remainder 6 ?
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The number when divided by 9, 11, 13 leaving remainder 6 = (i.c.m. of 9, 11, 13) + 6 = 1293
Required least number = 1294 - 1293 = 1.Correct Option: B
The number when divided by 9, 11, 13 leaving remainder 6 = (i.c.m. of 9, 11, 13) + 6 = 1293
Required least number = 1294 - 1293 = 1.
- The least number, which when divided by 16, 18 and 21 leaves the remainder 3, 5 and 8 respectively, is ?
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Here (16 - 3) = 13,
(18 - 5) = 13 and
(21 - 8 ) = 13
So, required number = (L . C . M of 16, 18, 21) - 13
= (1008 - 13)
= 995Correct Option: C
Here (16 - 3) = 13,
(18 - 5) = 13 and
(21 - 8 ) = 13
So, required number = (L . C . M of 16, 18, 21) - 13
= (1008 - 13)
= 995
- The greatest number of four digits which is divisible by each one of the numbers 12, 18 21 and 28 is ?
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Required number is divisible by the L . C . M of 12, 18, 21, 28 i.e 252.
Correct Option: C
Required number is divisible by the L . C . M of 12, 18, 21, 28 i.e 252.
Now, greatest number of four digits = 9999
On dividing 9999 by 252, the remainder is 171
∴ Required number = (9999 - 171) = 9828.
- The least number which when divided by 15, 27, 35 and 42, leaves in each case a remainder 7 is ?
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Required Number = (LCM of 15, 27, 35 and 42) + 7
Correct Option: B
Required Number = (LCM of 15, 27, 35 and 42) + 7
= 1890 + 7
= 1897
- The measuring rods are 64 cm, 80 cm and 96 cm in length. The least length of cloth that can be measured exact number of times using any one of the above rods bis ?
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Required length = L. C . M of (64, 80, 96) cm
Correct Option: C
Required length = L. C . M of (64, 80, 96) cm
= 960 cm
= 9.60 m.
