TCY - LCM HCF.ppt
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Transcript of TCY - LCM HCF.ppt
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App l ications o f LCM & HCF
Greatest Number that will leave no remainder when divides a, b and c
Required number = HCF of a, b and c
A shopkeeper has three cakes of weight 18 kg, 45 kg and 36 kg. If hewants to make these cakes into pieces of equal weight withoutwastage, what is the maximum possible weight of each piece?
(1) 1 (2) 9 (3) 12 (4) 13
Example
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The greatest number that will divide a, b & c leavingremainderx, y & z respectively
Required number = HCF of{(a x), (b y), (c z)}
What is the greatest number that divide 20, 50, and 40leaving 2, 5 and 4 as remainder?
Here a x=
b y=
c
z=Required Number =
App l ications o f LCM & HCF
Example
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To find the greatest number that will divide x, y and z leaving thesame remainderr in each case.
Required number = HCF of (x r), (y r) and (z r)
Find the greatest number which will divide 369, 449, 689,5009 and 729 so as to leave the remainder 9 in each case
(A) 2 (B) 49 (C) 35 (D) 40
Required Number is
HCF of {(369-9), (449-9), (689-9), (5009 9), (729 9)}= HCF of {360, 440, 680, 5000, 720}
= 40
App l ications o f LCM & HCF
Example
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To find the greatest number that will divide x, y and zleaving the same remainder in each case.
Required number = HCF of |x y|, |y z| and |z x|
What is the greatest number that will divide 1305, 4665 and
6905 leaving in each case the same remainder? Also
calculate the remainder.
(1) 1210, 158 (2) 1120, 158
(3) 1120, 185 (4) 1210, 185
App l ications o f LCM & HCF
Example
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Solut ion
Here we have
|4665 1305|, |6905 4665|, |6905 1305|
= 3360, 2240, 5600
= 1120 x 3, 1120 x 2, 1120 x 5Required number = HCF of (3360, 2240, 5600) = 1120
To calculate Remainder
1305 = 1120 x 1 + 185
So the Remainder = 185
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Least number which is exactly divisible by a, b, c
Required number = LCM of x, y and z
Sequence = n x LCM
(Where n is a natural Number)
Find the greatest number of five digits which is divisible by
32, 36, 40, 42 and 48
(a) 999720 (b) 90702 (C) 90720 (d) 90730
App l ications o f LCM & HCF
Example
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Step II
Find greater number of 5 digit which multiple of 10080
9279
10080 99999
907209
Greatest number = 90720
LCM of (32, 36, 40, 42, 48) = 10080
Solut ion
Step I
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To find least number which when divided by a, b, c leavesr as a remainder
Required number= LCM of (a, b, c) + r
What is the smallest sum which a person can have such that
when he distributed @ Rs. 2.5 or Rs 20 or Rs 12 or Rs. 7.5 per
person in a group, he is always left with Rs. 2.00?
(A) Rs. 62 (B) Rs. 80 (C) Rs. 90 (D) Rs. 100
App l icat ions o f LCM & HCF
Example
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According to the problem the person must have the money
equal to the LCM of2.5, 20, 12 and 7.5 and the remainder
money always left.
Solut ion
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Least number which when divided by a, b, c leaves x, y, zas remainder, such that a x = b y = c z = k (say)
Required number = LCM of (a, b, c) k
What is the greatest number of 4 digits that when dividedby the numbers 6, 9, 12, 17 leaves 5, 8, 11, 16 asremainders respectively?
(a) 9791 (b) 9793 (c) 9895 (d) 9497
App l icat ions o f LCM & HCF
Example
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Step 1 Here,
6 5 = 9 8 = 12 11= 17 16 = 1 = K (let)
Step 2 LCM of 6, 9, 12, 17 = 17 x 9 x 4 = 17 x 36 = 612
Step 3 Find Greatest 4 digit number which is multiple of 612
612 9999
612
3879
3672
207
16
Greatest Number= 9999 207 = 9792
Step 4 Required number = (LCM) n - K
= 9792 - 1 = 9791
Solut ion
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Thank you !!