Question
span >The LCM of six consecutive numbers is 420. The sum of the first and fourth numbers is equal to the sixth number. What is the product of six numbers?
Therefore, 420 = 2 × 2 × × 3 × 5 × 7 i.e, numbers are 2, 3, 4, 5, 6 and 7 Therefore, products is = 2 × 3 × 4 × 5 × 6 × 7 = 5040 Alternate method: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 Given that Sum of the first and fourth numbers is equal to the sixth number so, x + x + 3 = x + 5 x = 2 numbers are 2, 3, 4, 5, 6 and 7 Therefore, products is = 2 × 3 × 4 × 5 × 6 × 7 = 5040More HCF and LCM Questions
- How many pairs of natural numbers (x, y) exist such that x>y and the product of x, y and HCF (x, y) = 2520? solve this
- The HCF of 5453 and 6409 is 221, their LCM is:
- The LCM of two numbers is 240, and they are in the ratio 3:5. Determine the sum of these numbers.
- Three numbers a, b and c are co-prime to each other such that ab = 63 and bc = 77. Find the value of (a + b + c).
- Three numbers a, b and c are co-prime to each other such that ab = 115 and bc = 253. Find the value of (a + b + c).
- The H.C.F of two numbers is 3 and their L.C.M is 782. If one of the numbers is 34, find the other?
- Find the difference between sum of digits of LCM and HCF of 16, 40 and 64.
- Three numbers a, b and c are co-prime to each other such that ab = 76 and bc = 133. Find the value of (a + b + c).
- Three numbers a, b and c are co-prime to each other such that ab = 34 and bc = 51. Find the value of (a + b + c).
- What is the greatest number which divides 18, 29, and 40 and gives the remainder as 2, 3, and 4 respectively?
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