LCM & HCF- Tricks

 Trick-1

  • As learned in the previous video, the greatest number that will exactly divide x, y, & z is the HCF of x, y, & z.

  • If asked to find out the greatest number that will divide x, y, & z leaving reminders a, b, & c, respectively, the number would be HCF of (x-a), (y-b), and (z-c).

Example- Find the greatest number that will divide the 204 and 327 leaving remainders 4 and 7, respectively.

Solution: Greatest number will be HCF of (204-4) and (327-7)

HCF of 200 and 320 = 40

Therefore, 40 will divide 204 and 327 leaving remainders 4 and 7, respectively.

 

Trick-2

  • As learned in the previous video, the least number which when divided by x, y, and z leave no remainder is LCM of x, y, and z.
    • The least number which when divided by x, y, and z leave remainders a, b and c, respectively is given by [(LCM of x, y, & z) - k]. Where, k = x-a = y-b = z-c

Example- Find the least number divided by 12, 15, and 20 leaves remainders 4, 7, and 12, respectively.

As per the formula above, k = 12-4 = 15-7 = 20-12, the least number will be [(LCM of 12, 15, & 20) - 8]

LCM of 12, 15, & 20 will be 60. And the least number will be 60-8 = 52

Therefore, 52 is the least number divided by 12, 15, & 20 leaves remainders 4, 7, and 12, respectively.

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