Q. The quotient of the least common multiple of the first 46 natural numbers divided by the least common multiple of the first 43 natural numbers

• Given LCM of 1st 46 natural numbers to LCM of 1st 43 natural numbers
  therefore (1*2*3.....*46)/(1*2*3......*43)=LCM of(44,45,46)=45540
  
• 11 years agoHelpfull: Yes(15) No(6)
• At first natural no's are 1, 2 3,....
  L.C.M OF (1,2,3...46)=(2^5 * 3^3 * 5^2 * 7 * 11 * 13 * 17 * 19 * 23 *29 *31 *37 * 41* 43)
  BECAUSE l.c.m is generally the highest power of common prime factor...
  so L.C.M OF (1,2,3...43)=(2^5 * 3^3 * 5^2 * 7 * 11 * 13 * 17 * 19 * 23 *29 *31 *37 * 41* 43)..
  lcm of both 46 no and 43 no are same because they have same prime no... and same no of prime factors...
  Ans:: since Nr and Dr. are same
  (L.C.M oF 46 NO'S)/(L.C.M oF 46 NO'S)=1
  ANS=1
• 11 years agoHelpfull: Yes(13) No(2)
• the lcm of first 43 numbers is the product of the numbers which are highest exponent of the prime numbers in the given number set. Both of the number series have same lcm that is 2^5*3^3*5^2*7*11*13*17*19*23*29*31*37*41*43. Therefore the quotient is 1.
• 11 years agoHelpfull: Yes(8) No(4)
• 264
  46*45/43*42
• 11 years agoHelpfull: Yes(0) No(0)