The lcm of two consecutive even number is 180. find the numbers?
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Answer:
Step-by-step explanation:Let’s assume the two terms:1st term : 2x2nd term : 2x + 2There is a rule which states thatIf ‘a’ and ‘b’ are two numbers, then their product is equal to the product of their LCM and HCF.i.e,a∗b=HCF∗LCM - (i)We can logically say that the HCF of any two consecutive even numbers is always equal to ‘2’ provided that the smallest no. is at least ‘2’.i.e.,HCF of ‘2x’ and ‘2x + 2’ is ‘2’ - (ii)Therefore,from (i) and (ii),2x∗(2x+2)= HCF * LCM2x∗(2x+2)=2∗180x∗(2x+2)=1802x2+2x−180=0Solving the quadratic equation we get,x=9,−10(we discard -10 since it is negative)Therefore, the numbers are2∗9=18 (1st no.)2∗9+2=18+2=20 (2nd no.)Answer : 18,20Thank You,Hope this help U
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