UPSC CDS 2 2021 Math Paper

The time interval when they will meet next at the starting point is the LCM (20, 30 and 35 ).
Thus, the prime factorisation of 20,30 and 35 is
‌20=2×2×5=(2)2×(5)1,
30=2‌×3×5=(2)1×(3)1×(5)1
‌ and ‌35‌‌=5×7=(5)1×(7)1
‌ LCM ‌(20,30,35)‌
‌‌=(2)2×(3)1×(5)1×(7)1
‌‌=12×35
‌‌=420min
‌‌=‌

420

60

h=7h
Hence, all three runners will next meet after 7h at the starting point.