the number between 800 and 900 divisible completely by 13 and 17 is
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221 is the L.C.M. of 13 and 17. 800 is the lower limit as the no. you have to derive will be greater than or equall to 800. Again the upprer limit is 900 . as the no. you have to derive will not cross 900. so the no. will be between 800 and 900.
The no. will be a multiple of the L.C.M. we simply devide the lower limit and upper lmit by the L.C.M. to get the multiple.
In first case the quotient is 3 .
In second case The quotient is 4.
if we multiply the L.C.M. by 5 it will cross 900. The upper limit.
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Answer: STEP 1. LCM OF 13 AND 17 = 13×17 = 221.
STEP 2. SO, THE MULTIPLE OF 221 BETWEEN 800 AND 900 WILL BE DIVISIBLE BY 13 AND 17.
STEP 3. WHEN WE DIVIDE LOWEST NUMBER 800 BY 221.
STEP 4. NOW REMINDER = 137.
STEP 5. NOW WE SUBTRACT FROM LCM TO REMINDER = 221 - 137 = 84.
STEP 6. NOW REQUIRED NUMBER = (LOWEST NO + SUBTRACT NUMBER) = 800+84 =884 (THIS NO IS DIVIDED BY BOTH NUMBER 13 AND 17.
OR,
STEP 3. WHEN WE DIVIDED GREATEST NUMBER 900 BY 221.
STEP 4. NOW REMINDER = 16.
STEP 5. NOW REQUIRED NUMBER DIVIDED BY 13 AND 17 = (GREATEST NUMBER - REMINDER) = 900 - 16 = 884 ANSWER.
Step-by-step explanation:
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