The sum of two number is ’55’ and H.C.F. and L.C.M of these number are ‘5’ and ‘150’ respectively. What will be the numbers ?
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Solution
Let number are '5a' and '5b'
5a + 5b = 55
and a + b = 11 .....(i)
5ab = 150
ab = 30
So the number are 5 × 5 and 5 × 6 = 25, 30
What will be the Largest size of rod that can be used to measure the size of lengths 1.95 meters, 3 meters and 450 cm ?
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Solution
The Required length =
HCF of 1.95 meter, 3 meter and 450 cm
H.C.F. of (195, 300, 450)
= 15 cm = 0.15 meter
On dividing a number by 8, 9 and 11 we get 2 as remainder. What will be the smallest integer ?
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Solution
Required number is LCM of (8, 9 and 11) + 2
⇒ 792 + 2 = 794
On dividing a number by 5, 6 and 7 we get 3, 4 and 5 as remainder respectively. Find the number.
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Solution
Required number will
LCM of (5, 6, 7) – 2
= 210 - 2 = 208.
Which is the Largest among the following ?
, , ,
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Solution
Multiplying by LCM of denominators of Powers.
= (3)6, (4)4, (5)3, (2)6
= 729, 256, 125, 64
So Largest number =
What will be the sum of reciprocals of L.C.M and HCF of the terms 1 1 half comma space 2 1 third ?
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Solution
Terms are and
=
HCF = , LCM = 21
Sum of Reciprocals =
The L.C.M. of terms 22 × 33 × 55 × 77 and 72 ×53 × 35 × 27 will be?
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Solution
The LCM would be 27 × 35 × 55 × 77
Two numbers are in the ratio of 5 : 6 and the LCM is 900. What will be difference of the numbers ?
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Solution
Let the numbers are 5x and 6x
LCM ⇒ 5 × 6 × x = 900
x = 30
Difference = (6 – 5) 30 = 30
What will be the greatest number which on dividing 1657 and 2037 leaves remainder 6 and 5 respectively ?
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Solution
The required numbers is
HCF of (1657 – 6) and (2037 – 5)
⇒ HCF of (1651, 2032)
= 127
The LCM of terms and will be : –
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Solution
By comparing x = 64.
,
So. LCM is or = 8.