LCM and HCF
 Three tankers contain 403 litres, 434 litres, 465 litres of diesel respectively. Then the maximum capacity of a container that can measure the diesel of the three containers exact number of times is

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Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465Correct Option: A
Greatest capacity of measuring vessel
= HCF of 403 litres, 434 litres and 465 litres
First of all we find HCF of 403 and 434
Again , HCF of 31 and 465
∴ Greatest capacity of measuring vessel = 31 litres
 The greatest number that will divide 729 and 901 leaving remainders 9 and 5 respectively, is

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We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16Correct Option: B
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of (729 – 9) = 720 and (901 – 5) = 896
H.C.F = 16
Hence , required answer = 16.
 The greatest number by which 2300 and 3500 are divided leaving the remainders of 32 and 56 respectively, is

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As we know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 2300 – 32 = 2268 and 3500 – 56 = 3444Correct Option: D
As we know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 2300 – 32 = 2268 and 3500 – 56 = 3444
∴ HCF = 84
Hence , Required number = 84
 Find the greatest number which will exactly divide 200 and 320.

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Firstly , We find HCF of 200 and 320
Required number = HCF of 200 and 320Correct Option: D
Required number = HCF of 200 and 320
Firstly , We find HCF of 200 and 320
Required number = HCF of 200 and 320 = 40
 The greatest number that divides 411, 684, 821 and leaves 3, 4 and 5 as remainders, respectively, is

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We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 411 – 3 = 408; 684 – 4 = 680 and 821 – 5 = 816
HCF of 408 and 816 = 408
HCF of 408 and 680
∴ Required number = HCF of 408 and 680Correct Option: C
We know that the largest number which when divide the numbers a, b and c give remainders as p, q, r respectively is given by H.C.F. of (a – p), (b – q) and (c – r).
Required number = HCF of 411 – 3 = 408; 684 – 4 = 680 and 821 – 5 = 816
HCF of 408 and 816 = 408
HCF of 408 and 680
∴ Required number = HCF of 408 and 680
Hence , Required number = 136