## Skill Check VII: IITJEE Foundation Math

A) Find the LCM of the following numbers by the prime factorization method: (a) 24, 36 and 72 (b) 84 and 112 (c) 144 and 192 (d) 624 and 520 (e) 225 and 270 (f) 1008 and 1512 (g) 2310, 1540, and 770 (h) 840, 504, and 672 (i) 528, 396, and 352 (j) 6552, 4368, and 9828.

B) Find the LCM of the following numbers by the common division method: (a) 336 and 224 (b) 840 and1260 (c) 630 and 840 and 504 (d) 864, 1296, and 576 (e) 144, 216, and 384 (f) 1764, 1176, and 2352 (g) 260, 390, 156, and 104 (h) 1170, 780, 1755, and 2340 (i) 2520, 1680, 3780, and 3024 (j) 2730, 1950, 3822, and 1820.

C) Find the smallest number that is exactly divisible by 2016 and 3024.

D) Find the greatest 5-digit number that is exactly divisible by 420, 490, and 280.

E) Find the smallest 6-digit number which, when divided by 96, 144, 72, and 192, leaves exactly 8 as a remainder.

F) The LCM of two coprime numbers is 70560. If one of the numbers is 245, find the other number.

G) The LCM of 42 and another number is 168. If the HCF of the two numbers is 14, find the other number.

H) Four bells begin to toll together. The bells tolls after 8, 10, 12, and 15 seconds, respectively. After how long will all four bells toll together?

I) A toy soldier salutes after taking 14 steps while another salutes after every 21 steps. If both toy soldiers take a step every second, how long will it take for the toy soldiers to salute together five times after starting off together?

Regards,

Nalin Pithwa

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