Question

Find the lcm of (210)^12, (3003)^12

Answer 1

Given integers,
(210)¹² and (3003)¹²
Prime factorizations of,
(210)¹²=(2×3×5×7)¹²

(210)¹²=2¹²×3¹²×5¹²×7¹²

(3003)¹²=(3×7×11×13)¹²

(3003)¹²=3¹²×7¹²×11¹²×13¹²

LCM =product of each prime factor of highest power.
LCM=2¹²×3¹²×5¹²×7¹²×11¹²×13¹²

LCM=(2×3×5×7×11×13)¹²

LCM=(30030)¹²
Hence LCM of (210)¹² and (3003)¹² is equals to (30030)¹².

Answer 2

Given,
(210)¹² and (3003)¹²

We can write,

(210)¹²=(2*3*5*7)¹²

(210)¹²=2¹²*3¹²*5¹²*7¹²

(3003)¹²=(3*7*11*13)¹²

(3003)¹²=3¹²*7¹²*11¹²*13¹²

LCM of the numbers=2¹²*3¹²*5¹²*7¹²*11¹²*13¹²

LCM=(2*3*5*7*11*13)¹²

LCM=(30030)¹²

LCM of (210)¹² and (3003)¹² is (30030)¹²