Solved Problems On HCF &LCM AND Tricks

H.C.F and L.C.M of Numbers

1.  Find the L.C.M of 22 * 33 * 5 * 72, 23 * 32 * 52 * 74, 2 * 3 * 53 * 7 * 11

Answer: 2561
Explanation:
L.C.M = Product of highest powers of 2, 3, 5, 7 and 11.
= 23 * 33 * 53 * 74 * 11
= ( 2 * 2 * 2 ) * ( 3 * 3 * 3 ) * ( 5 * 5 * 5 ) * ( 7 * 7 * 7 * 7 )
= ( 8 ) + ( 27 ) + ( 125 ) + ( 2401 )
= 2561.


2.  Find the H.C.F of 108, 288 and 360?

Answer: 36
Explanation:
⇒ 108 = 22 * 33
⇒ 288 = 25 * 32
⇒ 360 = 23 * 5 * 32
H.C.F = 22 * 32
= 36.


3.  Find the greatest possible length which can be used to measure exactly the lengths 4m 95cm, 9m, 16m 65cm?

Answer: 45cm
Explanation:
Required length = H.C.F of 4m 95cm, 9m and 16m 65cm. ( ∴ 1 metre = 100 cm )
= H.C.F of 495cm, 900cm, 1665cm.
∴ 495 = 32 * 5 * 11
∴ 900 = 22 * 32 * 52
∴ 1665 = 32 * 5 * 37
H.C.F = 32 * 5
= 45cm
Hence, required length = 45cm.


4.  Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Find their H.C.F.?

Answer: 20
Explanation:
Let the numbers be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
⇒ 12x = 240
⇒ x = 240 / 12
= 20.

5.  The H.C.F. of two numbers is 5 and their L.C.M. is 150. If one of the numbers is 25, find the other number?

Answer: 30
Explanation:
Product of two numbers = Product of their HCF and LCM.
Let one number = x
⇒ ( 25x * x ) = ( 5 * 150 )
⇒ x = ( 5 * 150 ) / 25
= 30.


6.  If HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?

Answer: 33
Explanation:
Let the numbers be 11a and 11b
⇒ ( 11a * 11b ) = 363 ⇒ 121ab = 363
⇒ ab = 363 / 121
⇒ ab = 3
Co primes with product 3 = ( 1, 3 )
Hence the numbers with HCF 11 and product 363
= ( 11 * 1, 11 * 3 )
= ( 11, 33 )
Hence numbers are 11 and 33
The greater number = 33.


7.  Least number which when divided by 35,45,55 and leaves remainder 18,28,38 is?

Answer: 3448
Explanation:
Difference between every divisor and remainder is same = 17
Required number = l.c.m. of ( 35, 45, 55 ) - 17
= ( 3465 - 17 )
= 3448.

8.  Find the largest number which divides 62,132,237 to leave the same reminder ?

Answer: 35
Explanation:
Trick is HCF = ( 237 - 132 ), ( 132 - 62 ), ( 237 - 62 )
= HCF of ( 70, 105, 175 )
= 35.

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